// QuantumStates.java (C) 2002 by Paul Falstad, www.falstad.com import java.awt.*; import java.applet.Applet; import java.util.Vector; import java.util.Random; import java.lang.Math; import java.awt.event.*; import java.text.DecimalFormat; import java.text.NumberFormat; import org.netlib.util.*; import org.netlib.lapack.Dstedc; class QuantumStatesCanvas extends Canvas { QuantumStatesFrame pg; QuantumStatesCanvas(QuantumStatesFrame p) { pg = p; } public Dimension getPreferredSize() { return new Dimension(300,400); } public void update(Graphics g) { pg.updateQuantumStates(g); } public void paint(Graphics g) { pg.updateQuantumStates(g); } }; class QuantumStatesLayout implements LayoutManager { public QuantumStatesLayout() {} public void addLayoutComponent(String name, Component c) {} public void removeLayoutComponent(Component c) {} public Dimension preferredLayoutSize(Container target) { return new Dimension(500, 500); } public Dimension minimumLayoutSize(Container target) { return new Dimension(100,100); } public void layoutContainer(Container target) { int barwidth = 0; int i; for (i = 1; i < target.getComponentCount(); i++) { Component m = target.getComponent(i); if (m.isVisible()) { Dimension d = m.getPreferredSize(); if (d.width > barwidth) barwidth = d.width; } } Insets insets = target.insets(); int targetw = target.size().width - insets.left - insets.right; int cw = targetw-barwidth; int targeth = target.size().height - (insets.top+insets.bottom); target.getComponent(0).move(insets.left, insets.top); target.getComponent(0).resize(cw, targeth); cw += insets.left; int h = insets.top; for (i = 1; i < target.getComponentCount(); i++) { Component m = target.getComponent(i); if (m.isVisible()) { Dimension d = m.getPreferredSize(); if (m instanceof Scrollbar || m instanceof DecentScrollbar) d.width = barwidth; if (m instanceof Choice && d.width > barwidth) d.width = barwidth; if (m instanceof Label) { h += d.height/5; d.width = barwidth; } m.move(cw, h); m.resize(d.width, d.height); h += d.height; } } } }; public class QuantumStates extends Applet implements ComponentListener { QuantumStatesFrame qf; void destroyFrame() { if (qf != null) qf.dispose(); qf = null; repaint(); } boolean started = false; public void init() { addComponentListener(this); } void showFrame() { if (qf == null) { started = true; qf = new QuantumStatesFrame(this); qf.init(); repaint(); } } public void paint(Graphics g) { String s = "Applet is open in a separate window."; if (!started) s = "Applet is starting."; else if (qf == null) s = "Applet is finished."; else qf.show(); g.drawString(s, 10, 30); } public void componentHidden(ComponentEvent e){} public void componentMoved(ComponentEvent e){} public void componentShown(ComponentEvent e) { showFrame(); } public void componentResized(ComponentEvent e) {} public void destroy() { if (qf != null) qf.dispose(); qf = null; repaint(); } }; class QuantumStatesFrame extends Frame implements ComponentListener, ActionListener, MouseMotionListener, MouseListener, ItemListener, DecentScrollbarListener { Thread engine = null; Dimension winSize; Image dbimage; Random random; int stateCount; int elevelCount; int maxStateCount = 500; int sampleCount = 80; int pSampleCount; double modes[][]; double modesLeft[][]; public static final double epsilon = .00001; public static final double epsilon2 = .003; public static final double phasorBaseEnergy = 1; public static final double infiniteEnergy = 1000; public String getAppletInfo() { return "QuantumStates by Paul Falstad"; } Button blankButton; Button groundButton; Button normalizeButton; Button maximizeButton; Button rescaleButton; Checkbox stoppedCheck; CheckboxMenuItem eCheckItem; CheckboxMenuItem xCheckItem; CheckboxMenuItem pCheckItem; CheckboxMenuItem densityCheckItem; CheckboxMenuItem sumAllCheckItem; CheckboxMenuItem parityCheckItem; CheckboxMenuItem currentCheckItem; CheckboxMenuItem leftRightCheckItem; CheckboxMenuItem infoCheckItem; CheckboxMenuItem statesCheckItem; CheckboxMenuItem expectCheckItem; CheckboxMenuItem uncertaintyCheckItem; CheckboxMenuItem probCheckItem; CheckboxMenuItem probPhaseCheckItem; CheckboxMenuItem reImCheckItem; CheckboxMenuItem magPhaseCheckItem; CheckboxMenuItem alwaysNormItem; CheckboxMenuItem alwaysMaxItem; CheckboxMenuItem adiabaticItem; Menu waveFunctionMenu; MenuItem measureEItem; MenuItem measureXItem; MenuItem exitItem; Choice mouseChooser; Choice setupChooser; Vector setupList; Setup setup; DecentScrollbar forceBar, speedBar, resBar; DecentScrollbar massBar, aux1Bar, aux2Bar, aux3Bar; Label aux1Label, aux2Label, aux3Label; View viewPotential, viewX, viewP, viewParity, viewStates, viewSumAll, viewDensity, viewCurrent, viewLeft, viewRight, viewInfo; View viewList[]; int viewCount; double magcoef[]; double phasecoef[]; double phasecoefcos[]; double phasecoefsin[]; double phasecoefadj[]; double elevels[]; double dispmax[]; static final double pi = 3.14159265358979323846; double step; double func[]; double funci[]; double pdata[], pdatar[], pdatai[], currentData[], parityData[]; double pot[]; double mass; int selectedCoef; int selectedPaneHandle; static final int stateBuffer = 5; double selectedPState; static final int SEL_NONE = 0; static final int SEL_POTENTIAL = 1; static final int SEL_X = 2; static final int SEL_P = 3; static final int SEL_STATES = 4; static final int SEL_HANDLE = 5; static final int MOUSE_EIGEN = 0; static final int MOUSE_EDIT = 1; static final int MOUSE_GAUSS = 2; static final int MOUSE_TRANSLATE = 3; int selection; int dragX, dragY; int xpoints[], ypoints[]; boolean dragging; boolean startup, selectGround; boolean statesChanged, adjustingStates, adjustingWaveFunc; boolean setupModified; double t; int pause; static final int phaseColorCount = 480; Color phaseColors[]; FFT fft; int getrand(int x) { int q = random.nextInt(); if (q < 0) q = -q; return q % x; } QuantumStatesCanvas cv; QuantumStates applet; NumberFormat showFormat; QuantumStatesFrame(QuantumStates a) { super("1-d Quantum States Applet v1.6a"); applet = a; } public void init() { startup = true; xpoints = new int[5]; ypoints = new int[5]; setupList = new Vector(); Setup s = new InfiniteWellSetup(); while (s != null) { setupList.addElement(s); s = s.createNext(); } selectedCoef = -1; setLayout(new QuantumStatesLayout()); cv = new QuantumStatesCanvas(this); cv.addComponentListener(this); cv.addMouseMotionListener(this); cv.addMouseListener(this); add(cv); MenuBar mb = new MenuBar(); Menu m = new Menu("File"); mb.add(m); m.add(exitItem = getMenuItem("Exit")); m = new Menu("View"); mb.add(m); m.add(eCheckItem = getCheckItem("Energy")); eCheckItem.setState(true); m.add(xCheckItem = getCheckItem("Position")); xCheckItem.setState(true); m.add(pCheckItem = getCheckItem("Momentum")); pCheckItem.setState(true); m.add(sumAllCheckItem = getCheckItem("Sum All States")); /*m.add(densityCheckItem = getCheckItem("Density of Levels")); densityCheckItem.setState(true);*/ m.add(parityCheckItem = getCheckItem("Parity")); m.add(currentCheckItem = getCheckItem("Probability Current")); m.add(leftRightCheckItem = getCheckItem("Left/Right Waves")); m.add(infoCheckItem = getCheckItem("Values/Dimensions")); m.add(statesCheckItem = getCheckItem("State Phasors")); statesCheckItem.setState(true); m.addSeparator(); m.add(expectCheckItem = getCheckItem("Expectation Values")); expectCheckItem.setState(true); m.add(uncertaintyCheckItem = getCheckItem("Uncertainties")); Menu m2 = waveFunctionMenu = new Menu("Wave Function"); m.add(m2); m2.add(probCheckItem = getCheckItem("Probability")); m2.add(probPhaseCheckItem = getCheckItem("Probability + Phase")); probPhaseCheckItem.setState(true); m2.add(reImCheckItem = getCheckItem("Real + Imaginary Parts")); m2.add(magPhaseCheckItem = getCheckItem("Magnitude + Phase")); m = new Menu("Measure"); mb.add(m); m.add(measureEItem = getMenuItem("Measure Energy")); m.add(measureXItem = getMenuItem("Measure Position")); setMenuBar(mb); m = new Menu("Options"); mb.add(m); m.add(alwaysNormItem = getCheckItem("Always Normalize")); m.add(alwaysMaxItem = getCheckItem("Always Maximize")); m.add(adiabaticItem = getCheckItem("Adiabatic Changes")); adiabaticItem.setState(true); setMenuBar(mb); setupChooser = new Choice(); int i; for (i = 0; i != setupList.size(); i++) setupChooser.add("Setup: " + ((Setup) setupList.elementAt(i)).getName()); setup = (Setup) setupList.elementAt(0); setupChooser.addItemListener(this); add(setupChooser); mouseChooser = new Choice(); mouseChooser.add("Mouse = Set Eigenstate"); mouseChooser.add("Mouse = Edit Function"); mouseChooser.add("Mouse = Create Gaussian"); mouseChooser.add("Mouse = Translate Function"); mouseChooser.addItemListener(this); add(mouseChooser); mouseChooser.select(MOUSE_GAUSS); add(blankButton = new Button("Clear")); blankButton.addActionListener(this); add(normalizeButton = new Button("Normalize")); normalizeButton.addActionListener(this); add(maximizeButton = new Button("Maximize")); maximizeButton.addActionListener(this); add(groundButton = new Button("Ground State")); groundButton.addActionListener(this); add(rescaleButton = new Button("Rescale Graphs")); rescaleButton.addActionListener(this); stoppedCheck = new Checkbox("Stopped"); stoppedCheck.addItemListener(this); add(stoppedCheck); add(new Label("Simulation Speed", Label.CENTER)); add(speedBar = new DecentScrollbar(this, 80, 1, 300)); add(new Label("Resolution", Label.CENTER)); add(resBar = new DecentScrollbar(this, 260, 180, maxStateCount)); add(new Label("Particle Mass", Label.CENTER)); add(massBar = new DecentScrollbar(this, 16, 1, 100)); add(aux1Label = new Label("Aux 1", Label.CENTER)); add(aux1Bar = new DecentScrollbar(this, 50, 1, 100)); add(aux2Label = new Label("Aux 2", Label.CENTER)); add(aux2Bar = new DecentScrollbar(this, 50, 1, 100)); add(aux3Label = new Label("Aux 3", Label.CENTER)); add(aux3Bar = new DecentScrollbar(this, 50, 1, 100)); try { String param = applet.getParameter("PAUSE"); if (param != null) pause = Integer.parseInt(param); } catch (Exception e) { } magcoef = new double[maxStateCount]; phasecoef = new double[maxStateCount]; phasecoefcos = new double[maxStateCount]; phasecoefsin = new double[maxStateCount]; phasecoefadj = new double[maxStateCount]; dispmax = new double[maxStateCount]; setResolution(); phaseColors = new Color[phaseColorCount+1]; for (i = 0; i != phaseColorCount; i++) { int pm = phaseColorCount/6; int a1 = i % pm; int a2 = a1*255/pm; int a3 = 255-a2; Color c = null; switch (i/pm) { case 0: c = new Color(255, a2, 0); break; case 1: c = new Color(a3, 255, 0); break; case 2: c = new Color(0, 255, a2); break; case 3: c = new Color(0, a3, 255); break; case 4: c = new Color(a2, 0, 255); break; case 5: c = new Color(255, 0, a3); break; } phaseColors[i] = c; } phaseColors[phaseColorCount] = phaseColors[0]; random = new Random(); reinit(); cv.setBackground(Color.black); cv.setForeground(Color.lightGray); showFormat = DecimalFormat.getInstance(); showFormat.setMaximumFractionDigits(2); resize(750, 600); handleResize(); Dimension x = getSize(); Dimension screen = getToolkit().getScreenSize(); setLocation((screen.width - x.width)/2, (screen.height - x.height)/2); show(); } MenuItem getMenuItem(String s) { MenuItem mi = new MenuItem(s); mi.addActionListener(this); return mi; } CheckboxMenuItem getCheckItem(String s) { CheckboxMenuItem mi = new CheckboxMenuItem(s); mi.addItemListener(this); return mi; } void reinit() { doSetup(); } void handleResize() { Dimension d = winSize = cv.getSize(); if (winSize.width == 0) return; int potsize = (viewPotential == null) ? 0 : viewPotential.height; int statesize = (viewStates == null) ? 50 : viewStates.height; viewX = viewP = viewParity = viewCurrent = viewLeft = viewRight = viewStates = viewPotential = viewInfo = viewSumAll = viewDensity = null; viewList = new View[20]; int i = 0; if (eCheckItem.getState()) viewList[i++] = viewPotential = new View(); /*if (densityCheckItem.getState()) viewList[i++] = viewDensity = new View();*/ if (xCheckItem.getState()) viewList[i++] = viewX = new View(); if (sumAllCheckItem.getState()) viewList[i++] = viewSumAll = new View(); if (pCheckItem.getState()) viewList[i++] = viewP = new View(); if (parityCheckItem.getState()) viewList[i++] = viewParity = new View(); if (currentCheckItem.getState()) viewList[i++] = viewCurrent = new View(); if (leftRightCheckItem.getState() && setup.allowLeftRight()) { viewList[i++] = viewLeft = new View(); viewList[i++] = viewRight = new View(); } if (infoCheckItem.getState()) viewList[i++] = viewInfo = new View(); if (statesCheckItem.getState()) viewList[i++] = viewStates = new View(); viewCount = i; int sizenum = viewCount; int toth = winSize.height; // preserve size of potential and state panes if possible if (potsize > 0 && viewPotential != null) { sizenum--; toth -= potsize; } if (statesize > 0 && viewStates != null) { sizenum--; toth -= statesize; } // info pane is fixed size int infosize = 4*15+5; if (viewInfo != null) { sizenum--; toth -= infosize; } int cury = 0; for (i = 0; i != viewCount; i++) { View v = viewList[i]; int h = toth/sizenum; if (v == viewPotential && potsize > 0) h = potsize; else if (v == viewStates && statesize > 0) h = statesize; else if (v == viewInfo) h = infosize; v.x = 0; v.width = winSize.width; v.y = cury; v.height = h; cury += h; } setGraphLines(); dbimage = createImage(d.width, d.height); } void setGraphLines() { int i; for (i = 0; i != viewCount; i++) { View v = viewList[i]; v.mid_y = v.y + v.height/2; v.ymult = .90*v.height/2; v.lower_y = (int) (v.mid_y+v.ymult); v.ymult2 = v.ymult*2; } } void doGround() { int x; for (x = 0; x != stateCount; x++) magcoef[x] = 0; magcoef[0] = 1; t = 0; rescaleGraphs(); } void doBlank() { t = 0; // workaround bug in IE if (winSize != null && winSize.width > 0) dbimage = createImage(winSize.width, winSize.height); int x; for (x = 0; x != sampleCount; x++) func[x] = funci[x] = 0; for (x = 0; x != stateCount; x++) magcoef[x] = 0; } void normalize() { double norm = 0; int i; for (i = 0; i != stateCount; i++) norm += magcoef[i]*magcoef[i]; if (norm == 0) return; double normmult = 1/Math.sqrt(norm); for (i = 0; i != stateCount; i++) magcoef[i] *= normmult; cv.repaint(pause); } void maximize() { int i; double maxm = 0; for (i = 0; i != stateCount; i++) if (magcoef[i] > maxm) maxm = magcoef[i]; if (maxm == 0) return; for (i = 0; i != stateCount; i++) magcoef[i] *= 1/maxm; cv.repaint(pause); } void rescaleGraphs() { int i; for (i = 0; i != viewCount; i++) viewList[i].scale = 0; } void transform() { int x, y; t = 0; for (y = 0; y != stateCount; y++) { double a = 0; double b = 0; for (x = 1; x != sampleCount; x++) { a += modes[y][x]*func[x]; b += modes[y][x]*funci[x]; } if (a < epsilon && a > -epsilon) a = 0; if (b < epsilon && b > -epsilon) b = 0; double r = Math.sqrt(a*a+b*b); magcoef[y] = r; double ph2 = Math.atan2(b, a); phasecoefadj[y] = ph2; phasecoef[y] = ph2; } if (alwaysNormItem.getState()) normalize(); if (alwaysMaxItem.getState()) maximize(); } void centerString(Graphics g, String s, int y) { FontMetrics fm = g.getFontMetrics(); g.drawString(s, (winSize.width-fm.stringWidth(s))/2, y); } public void paint(Graphics g) { cv.repaint(); } long lastTime; public void updateQuantumStates(Graphics realg) { Graphics g = dbimage.getGraphics(); if (winSize == null || winSize.width == 0) return; boolean allQuiet = true; if (!stoppedCheck.getState() && !dragging && !adjustingStates) { int val = speedBar.getValue(); double tadd = Math.exp(val/20.)*(.1/5); long sysTime = System.currentTimeMillis(); if (lastTime == 0) lastTime = sysTime; t += tadd * (sysTime-lastTime)*(1/17.); lastTime = sysTime; allQuiet = false; } else lastTime = 0; Color gray1 = new Color(76, 76, 76); Color gray2 = new Color(127, 127, 127); g.setColor(cv.getBackground()); g.fillRect(0, 0, winSize.width, winSize.height); g.setColor(cv.getForeground()); int i; int ox = -1, oy = -1; for (i = 1; i != viewCount; i++) { g.setColor(i == selectedPaneHandle ? Color.yellow : Color.gray); g.drawLine(0, viewList[i].y, winSize.width, viewList[i].y); } if (statesChanged) { cv.setCursor(Cursor.getPredefinedCursor(WAIT_CURSOR)); if (adjustingStates) genStates(false); else { realg.setColor(cv.getBackground()); FontMetrics fm = realg.getFontMetrics(); String cs = "Calculating..."; realg.fillRect(0, winSize.height-30, 20+fm.stringWidth(cs), 30); realg.setColor(Color.white); realg.drawString(cs, 10, winSize.height-10); genStates(true); if (!adiabaticItem.getState()) transform(); else rescaleGraphs(); } cv.setCursor(null); statesChanged = false; if (startup) { magcoef[0] = magcoef[1] = 1; startup = false; } else if (selectGround) { magcoef[0] = 1; selectGround = false; } } ox = -1; int j; double norm = 0; if (!adjustingStates) { for (j = 0; j != stateCount; j++) { if (magcoef[j] < epsilon && magcoef[j] > -epsilon) { magcoef[j] = phasecoef[j] = phasecoefadj[j] = 0; continue; } phasecoef[j] = (-(elevels[j]+phasorBaseEnergy)*t+phasecoefadj[j]) % (2*pi); if (phasecoef[j] > pi) phasecoef[j] -= 2*pi; else if (phasecoef[j] < -pi) phasecoef[j] += 2*pi; phasecoefcos[j] = Math.cos(phasecoef[j]); phasecoefsin[j] = Math.sin(phasecoef[j]); norm += magcoef[j]*magcoef[j]; } } double normmult2 = 1/norm; double normmult = Math.sqrt(normmult2); if (norm == 0) normmult = normmult2 = 0; if (viewPotential != null) { int mid_y = viewPotential.mid_y; double ymult = viewPotential.ymult; viewPotential.scale = 1; g.setColor(gray2); g.drawLine(winSize.width/2, mid_y-(int) ymult, winSize.width/2, mid_y+(int) ymult); g.setColor(Color.gray); for (i = 0; i != elevelCount; i++) { if (i == stateCount) g.setColor(Color.darkGray); double dy = elevels[i]; int y = mid_y - (int) (ymult * dy); g.drawLine(0, y, winSize.width, y); } g.setColor(Color.white); for (i = 0; i != sampleCount; i++) { int x = winSize.width * i / sampleCount; double dy = pot[i]; int y = mid_y - (int) (ymult * dy); if (ox != -1) g.drawLine(ox, oy, x, y); ox = x; oy = y; } // calculate expectation value of E if (!adjustingStates && norm != 0 && (expectCheckItem.getState() || uncertaintyCheckItem.getState())) { double expecte = 0; double expecte2 = 0; for (i = 0; i != stateCount; i++) { double prob = magcoef[i]*magcoef[i]*normmult2; expecte += prob*elevels[i]; expecte2 += prob*elevels[i]*elevels[i]; } double uncert = Math.sqrt(expecte2-expecte*expecte); if (uncertaintyCheckItem.getState()) { if (!(uncert >= 0)) uncert = 0; g.setColor(Color.blue); int y = mid_y - (int) (ymult * (expecte+uncert)); g.drawLine(0, y, winSize.width, y); y = mid_y - (int) (ymult * (expecte-uncert)); if (expecte-uncert >= -1) g.drawLine(0, y, winSize.width, y); } if (expectCheckItem.getState()) { int y = mid_y - (int) (ymult * expecte); g.setColor(Color.red); g.drawLine(0, y, winSize.width, y); } } if (selectedCoef != -1 && !dragging) { g.setColor(Color.yellow); int y = mid_y - (int) (ymult * elevels[selectedCoef]); g.drawLine(0, y, winSize.width, y); } } ox = -1; g.setColor(Color.white); double maxf = 0; double expectx = 0; if (!adjustingStates && !adjustingWaveFunc) { // calculate wave function for (i = 0; i != sampleCount; i++) { int x = winSize.width * i / sampleCount; double dr = 0, di = 0; for (j = 0; j != stateCount; j++) { dr += magcoef[j] * modes[j][i] * phasecoefcos[j]; di += magcoef[j] * modes[j][i] * phasecoefsin[j]; } dr *= normmult; di *= normmult; func[i] = dr; funci[i] = di; double dy = dr*dr+di*di; expectx += dy*x; if (dy > maxf) maxf = dy; } } else { for (i = 0; i != sampleCount; i++) { int x = winSize.width * i / sampleCount; double dr = func[i], di = funci[i]; double dy = dr*dr+di*di; expectx += dy*x; if (dy > maxf) maxf = dy; } } if (viewX != null) { // draw X representation int mid_y = viewX.mid_y; double ymult = viewX.ymult; drawFunction(g, viewX, func, funci, sampleCount, 0); if (selectedCoef != -1 && !dragging) { g.setColor(Color.yellow); ox = -1; for (i = 0; i != sampleCount; i++) { int x = winSize.width * i / sampleCount; double dy = modes[selectedCoef][i]/dispmax[selectedCoef]; int y = mid_y - (int) (ymult * dy); if (ox != -1) g.drawLine(ox, oy, x, y); ox = x; oy = y; } } if (selectedPState != 0) { g.setColor(Color.yellow); ox = -1; int s2 = sampleCount*2; for (i = 0; i != s2; i++) { int x = winSize.width * i / s2; double dy = Math.cos(selectedPState* (i-sampleCount)*.5); int y = mid_y - (int) (ymult * dy); if (ox != -1) g.drawLine(ox, oy, x, y); ox = x; oy = y; } } } if (viewP != null) { // draw P representation for (i = 0; i != pSampleCount*2; i++) pdata[i] = 0; for (i = 0; i != sampleCount; i++) { int ii = (i <= sampleCount/2) ? (sampleCount/2-i)*2 : (pSampleCount-(i-sampleCount/2))*2; pdata[ii] = func[sampleCount-1-i]; pdata[ii+1] = funci[sampleCount-1-i]; } fft.transform(pdata, false); double pnorm = 1/Math.sqrt(pSampleCount); for (i = 0; i != pSampleCount; i++) { int ii = (i <= pSampleCount/2) ? (pSampleCount/2-i)*2 : (pSampleCount-(i-pSampleCount/2))*2; pdatar[i] = pdata[ii]*pnorm; pdatai[i] = pdata[ii+1]*pnorm; } int offset = pSampleCount/4; drawFunction(g, viewP, pdatar, pdatai, pSampleCount/2, offset); } if (viewParity != null) { // draw parity graph double pplus = 0, pminus = 0; for (i = 0; i != sampleCount; i++) { double a1 = func[i]; double a2 = funci[i]; double b1 = func[sampleCount-1-i]; double b2 = funci[sampleCount-1-i]; double c1 = (a1+b1)*(a1+b1)+(a2+b2)*(a2+b2); double c2 = (a1-b1)*(a1-b1)+(a2-b2)*(a2-b2); pplus += c1; pminus += c2; } parityData[90] = Math.sqrt(pplus)/2; parityData[10] = Math.sqrt(pminus)/2; drawFunction(g, viewParity, parityData, null, 100, 0); } if (viewCurrent != null) { // draw probability current for (i = 0; i != sampleCount-1; i++) { double a1 = func[i+1]-func[i]; double a2 = funci[i+1]-funci[i]; currentData[i] = func[i]*a2 - funci[i]*a1; } drawFunction(g, viewCurrent, currentData, null, sampleCount, 0); } if (viewLeft != null && viewRight != null && !setupModified) { if (viewX != null) viewLeft.scale = viewRight.scale = viewX.scale; if (setup instanceof HarmonicOscillatorSetup) doOscLeftRight(g); else if (setup instanceof InfiniteWellSetup) doBoxLeftRight(g, normmult); } if (viewSumAll != null && !adjustingStates) { double sumx[] = new double[sampleCount]; for (j = 0; j != stateCount; j++) for (i = 0; i != sampleCount; i++) sumx[i] += modes[j][i]*modes[j][i]; drawFunction(g, viewSumAll, sumx, null, sampleCount, 0); } /*if (viewDensity != null) { double density[] = new double[20]; int dlen = density.length; for (i = 0; i != stateCount; i++) { int e = (int) (1+dlen*(elevels[i]+1)/2); if (e < dlen) density[e]++; } drawFunction(g, viewDensity, density, null, dlen, 0); }*/ if (viewInfo != null) { String s[] = new String[5]; setup.getInfo(s, 2); // calculate expectation value of E double expecte = 0; for (i = 0; i != stateCount; i++) { double prob = magcoef[i]*magcoef[i]*normmult2; expecte += prob*elevels[i]; } g.setColor(Color.white); s[0] = " = " + getEnergyText(expecte, true); // we're multiplying t times elevels[x] to get the phase angle. // if t*elevels[x] = realE realt/hbar, then realt = t elevels[x] hbar/realE. double realt = t*6.58212e-16/convertEnergy(1, false); s[1] = "t = " + getUnitText(realt, "s"); String massStr = ", m = " + getUnitText(mass, "eV") + "/c^2"; if (mass == .511e6) massStr += " (electron)"; s[0] += massStr; for (i = 0; s[i] != null; i++) { int y = (i+1)*15; if (y+4 < viewInfo.height) centerString(g, s[i], y+viewInfo.y); } } if (viewStates != null && !adjustingStates) { // draw state phasors stateColSize = winSize.width / 10; if (stateColSize < 20) stateColSize = 20; for (i = stateColSize-1; i >= 8; i--) { int ss = winSize.width/i; int h = ss*((stateCount+i-1)/i); if (h <= viewStates.height-stateBuffer) stateColSize = i; } stateSize = winSize.width/stateColSize; int ss2 = stateSize/2; for (i = 0; i != stateCount; i++) { int x = stateSize*(i % stateColSize)+ss2; int y = stateSize*(i / stateColSize)+ss2 + viewStates.y + stateBuffer; g.setColor(i == selectedCoef ? Color.yellow : (magcoef[i] == 0) ? gray2 : Color.white); g.drawOval(x-ss2, y-ss2, stateSize, stateSize); int xa = (int) (magcoef[i]*phasecoefcos[i]*ss2); int ya = (int) (-magcoef[i]*phasecoefsin[i]*ss2); g.drawLine(x, y, x+xa, y+ya); g.drawLine(x+xa-1, y+ya, x+xa+1, y+ya); g.drawLine(x+xa, y+ya-1, x+xa, y+ya+1); } } realg.drawImage(dbimage, 0, 0, this); if (!stoppedCheck.getState() && !allQuiet) cv.repaint(pause); } String getUnitText(double v, String u) { double va = Math.abs(v); if (va < 1e-17) return "0 " + u; if (va < 1e-12) return showFormat.format(v*1e15) + " f" + u; if (va < 1e-9) return showFormat.format(v*1e12) + " p" + u; if (va < 1e-6) return showFormat.format(v*1e9) + " n" + u; if (va < 1e-3) return showFormat.format(v*1e6) + " u" + u; if (va < 1) return showFormat.format(v*1e3) + " m" + u; if (va < 1e3) return showFormat.format(v) + " " + u; if (va < 1e6) return showFormat.format(v*1e-3) + " k" + u; if (va < 1e9) return showFormat.format(v*1e-6) + " M" + u; if (va < 1e12) return showFormat.format(v*1e-9) + " G" + u; if (va < 1e15) return showFormat.format(v*1e-12) + " T" + u; return v + " " + u; } String getEnergyText(double e, boolean abs) { return getUnitText(convertEnergy(e, abs), "eV"); } String getLengthText(double x) { // getEnergyText() assumes a 4 nm screen width return getUnitText(pointsToLength(x), "m"); } double pointsToLength(double x) { // getEnergyText() assumes a 4 nm screen width return 4e-9*x/(sampleCount-2.); } double convertEnergy(double e, boolean abs) { // ground state energy for an electron in a 4 nm infinite well (in eV) // (for 1 Angstrom, it's 37.603) double base = .023502; // the calculated ground state energy for a particle of default mass in a // well the full width of the window is 0.001891. So, if we assume the // window is 1 angstrom wide, then we multiply the elevels by base/.001891 to // get eV. if (abs) e += setup.getBaseEnergy(); return e*base/.0018801; } int stateColSize, stateSize; void drawFunction(Graphics g, View view, double fr[], double fi[], int count, int offset) { int i; double expectx = 0; double expectx2 = 0; double maxsq = 0; double tot = 0; int zero = winSize.width/2; for (i = 0; i != count; i++) { int x = winSize.width * i / (count-1); int ii = i+offset; double dr = fr[ii]; double di = (fi == null) ? 0 : fi[ii]; double dy = dr*dr+di*di; if (dy > maxsq) maxsq = dy; int dev = x-zero; expectx += dy*dev; expectx2 += dy*dev*dev; tot += dy; } expectx /= tot; expectx2 /= tot; double maxnm = Math.sqrt(maxsq); double uncert = Math.sqrt(expectx2-expectx*expectx); int ox = -1, oy = 0; double bestscale = 0; if (fi != null && (probCheckItem.getState() || probPhaseCheckItem.getState())) bestscale = 1/maxsq; else bestscale = 1/maxnm; if (!adjustingWaveFunc) { // adjust scale view.scale *= 1.001; if (view.scale > bestscale || view.scale == 0) view.scale = bestscale; if (view.scale > 1e8) view.scale = 1e8; } g.setColor(Color.gray); /* double scaler = 1e-10; while (scaler*view.scale*view.ymult*600 < view.height) scaler *= 10; System.out.print(scaler + "\n"); for (i = 0; i != 20; i++) { int y = (int) (view.ymult * i * view.scale * scaler * 10); System.out.print(i + " " + y + "\n"); if (y > view.height/2) break; g.drawLine(winSize.width-5, view.mid_y - y, winSize.width, view.mid_y - y); } */ if ((probCheckItem.getState() || probPhaseCheckItem.getState() || magPhaseCheckItem.getState()) && fi != null) { // draw probability or magnitude g.setColor(Color.white); double mult = view.ymult2*view.scale; for (i = 0; i != count; i++) { int x = winSize.width * i / (count-1); double dy = 0; int ii = i+offset; if (!magPhaseCheckItem.getState()) dy = (fr[ii]*fr[ii]+fi[ii]*fi[ii]); else dy = Math.sqrt(fr[ii]*fr[ii]+fi[ii]*fi[ii]); if (!probCheckItem.getState()) { double ang = Math.atan2(fi[ii], fr[ii]); g.setColor(phaseColors[(int)((ang+pi)*phaseColorCount/(2*pi+.2))]); } int y = view.lower_y - (int) (mult * dy); if (y < view.y) y = view.y; if (ox != -1) { xpoints[0] = ox; ypoints[0] = view.lower_y+1; xpoints[1] = ox; ypoints[1] = oy; xpoints[2] = x; ypoints[2] = y; xpoints[3] = x; ypoints[3] = view.lower_y+1; g.fillPolygon(xpoints, ypoints, 4); } ox = x; oy = y; } } else { int mid_y = view.mid_y; double mult = view.ymult*view.scale; if (fi != null) { g.setColor(Color.blue); for (i = 0; i != count; i++) { int x = winSize.width * i / (count-1); int ii = i+offset; int y = mid_y - (int) (mult * fi[ii]); if (ox != -1) g.drawLine(ox, oy, x, y); ox = x; oy = y; } } g.setColor(Color.white); ox = -1; for (i = 0; i != count; i++) { int x = winSize.width * i / (count-1); int ii = i+offset; int y = mid_y - (int) (mult * fr[ii]); if (ox != -1) g.drawLine(ox, oy, x, y); ox = x; oy = y; } } if (maxsq > 0 && fi != null) { expectx += zero; if (uncertaintyCheckItem.getState()) { g.setColor(Color.blue); g.drawLine((int) (expectx-uncert), view.y, (int) (expectx-uncert), view.y+view.height); g.drawLine((int) (expectx+uncert), view.y, (int) (expectx+uncert), view.y+view.height); } if (expectCheckItem.getState()) { g.setColor(Color.red); g.drawLine((int) expectx, view.y, (int) expectx, view.y+view.height); } } } void doOscLeftRight(Graphics g) { int i; for (i = 0; i != pSampleCount*2; i++) pdata[i] = 0; for (i = 0; i != sampleCount; i++) { int ii = (i <= sampleCount/2) ? (sampleCount/2-i)*2 : (pSampleCount-(i-sampleCount/2))*2; pdata[ii] = func[i]; pdata[ii+1] = funci[i]; } fft.transform(pdata, false); for (i = 2; i != pSampleCount; i++) pdata[i] = 0; fft.transform(pdata, true); double pnorm = 1./pSampleCount; for (i = 0; i != sampleCount; i++) { int ii = (i <= sampleCount/2) ? (sampleCount/2-i)*2 : (pSampleCount-(i-sampleCount/2))*2; pdatar[i] = pdata[ii]*pnorm; pdatai[i] = pdata[ii+1]*pnorm; } drawFunction(g, viewLeft, pdatar, pdatai, sampleCount, 0); for (i = 0; i != sampleCount; i++) { pdatar[i] = func[i] -pdatar[i]; pdatai[i] = funci[i]-pdatai[i]; } drawFunction(g, viewRight, pdatar, pdatai, sampleCount, 0); } void doBoxLeftRight(Graphics g, double normmult) { if (adjustingStates) return; if (modesLeft == null) { // calculate imaginary part of left-moving waves // (modes[][] is real part) int width = ((InfiniteWellSetup) setup).getOffset()-1; modesLeft = new double[stateCount][sampleCount]; int i, j; for (i = 0; i != stateCount; i++) { int ni = i+1; double sgn = (modes[i][width] > 0) ? 1 : -1; double mult = sgn*dispmax[i]; double xmult = pi/(sampleCount-width*2-1); for (j = width; j != sampleCount-width; j++) { double xx = (j-width)*xmult; modesLeft[i][j] = Math.cos(xx*ni) * mult; } } } int i, j; normmult *= .5; for (i = 0; i != sampleCount; i++) { double dr = 0, di = 0; for (j = 0; j != stateCount; j++) { double a = magcoef[j]*phasecoefcos[j]; double b = magcoef[j]*phasecoefsin[j]; dr += modes[j][i]*a - modesLeft[j][i]*b; di += modes[j][i]*b + modesLeft[j][i]*a; } pdatar[i] = dr*normmult; pdatai[i] = di*normmult; } drawFunction(g, viewLeft, pdatar, pdatai, sampleCount, 0); for (i = 0; i != sampleCount; i++) { pdatar[i] = func[i] -pdatar[i]; pdatai[i] = funci[i]-pdatai[i]; } drawFunction(g, viewRight, pdatar, pdatai, sampleCount, 0); } void edit(MouseEvent e) { if (selection == SEL_NONE) return; int x = e.getX(); int y = e.getY(); switch (selection) { case SEL_HANDLE: editHandle(y); break; case SEL_STATES: editMag(x, y); break; default: editFunc(x, y); break; } } void editHandle(int y) { int dy = y-viewList[selectedPaneHandle].y; View upper = viewList[selectedPaneHandle-1]; View lower = viewList[selectedPaneHandle]; int minheight = 10; if (upper.height+dy < minheight || lower.height-dy < minheight) return; upper.height += dy; lower.height -= dy; lower.y += dy; setGraphLines(); cv.repaint(pause); } void editMag(int x, int y) { if (selectedCoef == -1) return; int ss2 = stateSize/2; int x0 = stateSize*(selectedCoef % stateColSize)+ss2; int y0 = stateSize*(selectedCoef / stateColSize)+ss2 + viewStates.y + stateBuffer; x -= x0; y -= y0; double mag = Math.sqrt(x*x+y*y)/ss2; double ang = Math.atan2(-y, x); double ang0 = (-(elevels[selectedCoef]+phasorBaseEnergy)*t) % (2*pi); if (mag > 10) mag = 0; if (mag > 1) mag = 1; magcoef[selectedCoef] = mag; phasecoefadj[selectedCoef] = (ang-ang0) % (2*pi); if (phasecoefadj[selectedCoef] > pi) phasecoefadj[selectedCoef] -= 2*pi; if (alwaysNormItem.getState()) normalize(); cv.repaint(pause); } void editFunc(int x, int y) { if (mouseChooser.getSelectedIndex() == MOUSE_EIGEN) { if (selection == SEL_X) { editXState(x, y); return; } if (selection == SEL_P) { editPState(x, y); return; } if (selection == SEL_POTENTIAL) { findStateByEnergy(y); enterSelectedState(); } return; } if (mouseChooser.getSelectedIndex() == MOUSE_GAUSS) { if (selection == SEL_X) editXGauss(x, y); if (selection == SEL_P) editPGauss(x, y); if (selection == SEL_POTENTIAL) { findStateByEnergy(y); enterSelectedState(); } return; } if (mouseChooser.getSelectedIndex() == MOUSE_TRANSLATE) { if (selection == SEL_X) translateXGauss(x); if (selection == SEL_P) translatePGauss(x); return; } if (selection == SEL_P) return; if (dragX == x) { editFuncPoint(x, y); dragY = y; } else { // need to draw a line from old x,y to new x,y and // call editFuncPoint for each point on that line. yuck. int x1 = (x < dragX) ? x : dragX; int y1 = (x < dragX) ? y : dragY; int x2 = (x > dragX) ? x : dragX; int y2 = (x > dragX) ? y : dragY; dragX = x; dragY = y; for (x = x1; x <= x2; x++) { y = y1+(y2-y1)*(x-x1)/(x2-x1); editFuncPoint(x, y); } } if (adjustingWaveFunc) { transform(); if (alwaysNormItem.getState()) normalize(); else maximize(); } } void editXGauss(int x, int y) { int i; int xi = x * sampleCount / winSize.width; double mult = Math.exp(-(y-viewX.mid_y)*.03-4); for (i = 0; i != sampleCount; i++) { int ii = i-xi; func[i] = Math.exp(-ii*ii*mult); funci[i] = 0; } transform(); if (alwaysNormItem.getState()) normalize(); else maximize(); rescaleGraphs(); } void editPGauss(int x, int y) { int i; int xi = x * sampleCount / winSize.width; double mult = Math.exp((y-viewP.mid_y)*.03-4); double p = getPState(x); int s2 = sampleCount/2; // rather than draw a gaussian and then transform it back to X, // we just draw a function on the X graph that looks like a gaussian // on the P graph. for (i = 0; i != sampleCount; i++) { int ii = i-s2; double n = Math.exp(-ii*ii*mult); func[i] = Math.cos(p*ii)*n; funci[i] = Math.sin(p*ii)*n; } selectedPState = 0; transform(); if (alwaysNormItem.getState()) normalize(); else maximize(); rescaleGraphs(); } void translateXGauss(int x) { int dx = x-dragX; if (dx == 0) return; dragX = x; int i; dx = dx*sampleCount / winSize.width; if (dx > 0) { for (i = sampleCount-dx-1; i >= 0; i--) { func [i+dx] = func [i]; funci[i+dx] = funci[i]; } } else { for (i = -dx; i != sampleCount; i++) { func [i+dx] = func [i]; funci[i+dx] = funci[i]; } } transform(); cv.repaint(pause); } void translatePGauss(int x) { double px = getPState(x) - getPState(dragX); dragX = x; int i; for (i = 0; i != sampleCount; i++) { double dr = Math.cos(px*i)*func [i] - Math.sin(px*i)*funci[i]; double di = Math.cos(px*i)*funci[i] + Math.sin(px*i)*func [i]; func [i] = dr; funci[i] = di; } transform(); cv.repaint(pause); } void editFuncPoint(int x, int y) { View v = (selection == SEL_X) ? viewX : viewPotential; int lox = x * sampleCount / winSize.width; int hix = ((x+1) * sampleCount-1) / winSize.width; double val = (v.mid_y - y) / v.ymult; double val2 = (v.lower_y - y) / v.ymult2; if (val > 1) val = 1; if (val < -1) val = -1; if (val2 > 1) val2 = 1; if (val2 < 0) val2 = 0; val /= v.scale; val2 /= v.scale; if (lox < 1) lox = 1; if (hix >= sampleCount-1) hix = sampleCount-2; for (; lox <= hix; lox++) { if (selection == SEL_POTENTIAL) { pot[lox] = val; setupModified = true; adjustingStates = statesChanged = true; } else { if (probCheckItem.getState() || probPhaseCheckItem.getState()) { double valnew = Math.sqrt(val2); double n = Math.sqrt(func[lox]*func[lox] + funci[lox]*funci[lox]); if (n == 0) { func[lox] = 1; n = 1; } // edit magnitude, preserving phase func[lox] = valnew*func[lox]/n; funci[lox] = valnew*funci[lox]/n; } else if (magPhaseCheckItem.getState()) { double n = Math.sqrt(func[lox]*func[lox] + funci[lox]*funci[lox]); if (n == 0) { func[lox] = 1; n = 1; } func[lox] = val2*func[lox]/n; funci[lox] = val2*funci[lox]/n; } else { func[lox] = val; } adjustingWaveFunc = true; } } cv.repaint(pause); } void editXState(int x, int y) { int ax = x * sampleCount / winSize.width; if (ax < 1 || ax >= sampleCount) return; int i; for (i = 0; i != sampleCount; i++) func[i] = funci[i] = 0; func[ax] = 1; transform(); rescaleGraphs(); if (!alwaysNormItem.getState()) maximize(); cv.repaint(pause); } double getPState(int x) { double p = (x * pSampleCount/2 / winSize.width) - pSampleCount/4; return p*pi/(pSampleCount/2); } void editPState(int x, int y) { double p = getPState(x); int i; int s2 = sampleCount/2; for (i = 0; i != sampleCount; i++) { func[i] = Math.cos(p*(i-s2)); funci[i] = Math.sin(p*(i-s2)); } transform(); rescaleGraphs(); if (!alwaysNormItem.getState()) maximize(); selectedPState = 0; cv.repaint(pause); } public void componentHidden(ComponentEvent e){} public void componentMoved(ComponentEvent e){} public void componentShown(ComponentEvent e) { cv.repaint(pause); } public void componentResized(ComponentEvent e) { handleResize(); cv.repaint(pause); } public void actionPerformed(ActionEvent e) { if (e.getSource() == exitItem) { applet.destroyFrame(); return; } cv.repaint(); if (e.getSource() == measureEItem) measureE(); if (e.getSource() == measureXItem) measureX(); if (e.getSource() == groundButton) doGround(); if (e.getSource() == blankButton) doBlank(); if (e.getSource() == normalizeButton) normalize(); if (e.getSource() == maximizeButton) maximize(); if (e.getSource() == rescaleButton) rescaleGraphs(); } public void scrollbarValueChanged(DecentScrollbar ds) { System.out.print(ds.getValue() + "\n"); if (ds == massBar) { statesChanged = adjustingStates = true; cv.repaint(pause); } if (ds == aux1Bar || ds == aux2Bar || ds == aux3Bar) { adjustingStates = true; setup.drawPotential(); statesChanged = true; cv.repaint(pause); } if (ds == resBar) adjustingStates = true; } public void scrollbarFinished(DecentScrollbar ds) { if (ds == resBar) { adjustingStates = false; setResolution(); reinit(); cv.repaint(pause); } if (ds == massBar || ds == aux1Bar || ds == aux2Bar || ds == aux3Bar) { adjustingStates = false; statesChanged = true; cv.repaint(pause); } } public boolean handleEvent(Event ev) { if (ev.id == Event.WINDOW_DESTROY) { applet.destroyFrame(); return true; } return super.handleEvent(ev); } void setResolution() { sampleCount = resBar.getValue(); sampleCount++; func = new double[sampleCount]; funci = new double[sampleCount]; pot = new double[sampleCount]; statesChanged = true; int ps = 8*sampleCount; pSampleCount = 1; while (pSampleCount < ps) pSampleCount *= 2; pdata = new double[pSampleCount*2]; pdatar = new double[pSampleCount]; pdatai = new double[pSampleCount]; parityData = new double[100]; currentData = new double[sampleCount]; fft = new FFT(pSampleCount); } void genStates(boolean getStates) { System.out.println("genstates"); statesChanged = false; int n = sampleCount; double d[] = new double[n]; double e[] = new double[n]; double z[] = new double[n*n]; int i, j; mass = massBar.getValue()*.02; double m1 = 1/(mass*1.006); mass *= .511e6 / .32; double maxpot = -20; // correct for finite resolution double rescorr = sampleCount/128.; m1 *= rescorr*rescorr; // express schroedinger's equation as a matrix equation // using finite differencing for (i = 0; i != n; i++) { if (i < n-1) e[i] = -m1; d[i] = 2*m1+pot[i]; if (pot[i] > maxpot) maxpot = pot[i]; int in = i*n; for (j = 0; j != n; j++) z[in+j] = 0; z[in+i] = 1; } double work[] = new double[1+4*n+n*n]; int iwork[] = new int[3+5*n]; intW info = new intW(0); // use LAPACK to find the eigenvalues and eigenvectors Dstedc.dstedc(getStates ? "I" : "N", n, d, 0, e, 0, z, 0, n, work, 0, work.length, iwork, 0, iwork.length, info); elevels = new double[n]; elevelCount = n; // now get the eigenvalues and sort them for (i = 0; i != n; i++) { /*if (i < n-1 && d[i] == d[i+1]) System.out.print("degeneracy! " + d[i] + "\n");*/ elevels[i] = d[i]; } int si, sj; // sort the elevels for (si = 1; si < n; si++) { double v = elevels[si]; sj = si; while (elevels[sj-1] > v) { elevels[sj] = elevels[sj-1]; sj--; if (sj <= 0) break; } elevels[sj] = v; } while (maxpot > 0 && elevels[elevelCount-1] > maxpot) elevelCount--; stateCount = elevelCount; int maxs = sampleCount*3/8; if (stateCount > maxs && getStates) stateCount = maxs; if (!getStates) return; // get the eigenstates modes = new double[stateCount][sampleCount]; for (i = 0; i != stateCount; i++) { for (j = 0; j != n; j++) if (elevels[i] == d[j]) break; if (j == n) { System.out.print("can't find elevels! " + i + " " + elevels[i] + "\n"); continue; } d[j] = -1; int k; dispmax[i] = 0; for (k = 0; k != n; k++) { modes[i][k] = z[j*n+k]; if (modes[i][k] > dispmax[i]) dispmax[i] = modes[i][k]; else if (-modes[i][k] > dispmax[i]) dispmax[i] = -modes[i][k]; } } modesLeft = null; // The energy levels calculated above for a harmonic oscillator are // not evenly spaced because of numerical error, so we force // them to be evenly spaced in order to get coherent states to work if (!setupModified) setup.fudgeLevels(); System.out.println("done"); } public void mouseDragged(MouseEvent e) { dragging = true; edit(e); } public void mouseMoved(MouseEvent e) { int x = e.getX(); int y = e.getY(); dragX = x; dragY = y; int oldCoef = selectedCoef; int oldSelection = selection; selectedCoef = -1; selectedPState = 0; selectedPaneHandle = -1; selection = 0; int i; for (i = 1; i != viewCount; i++) { int dy = y-viewList[i].y; if (dy >= -3 && dy <= 3) { selectedPaneHandle = i; selection = SEL_HANDLE; } } Cursor cs = null; if (selection == SEL_HANDLE) cs = Cursor.getPredefinedCursor(N_RESIZE_CURSOR); else if (viewX != null && viewX.contains(x, y)) selection = SEL_X; else if (viewP != null && viewP.contains(x, y)) { selection = SEL_P; selectedPState = getPState(x); cv.repaint(pause); } else if (viewPotential != null && viewPotential.contains(x, y)) { selection = SEL_POTENTIAL; if (mouseChooser.getSelectedIndex() != MOUSE_EDIT) findStateByEnergy(y); } else if (viewStates != null && viewStates.contains(x, y)) { int xi = x/stateSize; int yi = (y-(viewStates.y+stateBuffer))/stateSize; selectedCoef = xi+yi*stateColSize; if (selectedCoef >= stateCount) selectedCoef = -1; if (selectedCoef != -1) selection = SEL_STATES; } cv.setCursor(cs); if (selection != oldSelection || selectedCoef != oldCoef) cv.repaint(pause); } void findStateByEnergy(int y) { if (adjustingStates || statesChanged) return; int i; double dy = (viewPotential.mid_y-y)/viewPotential.ymult; double dist = 100; for (i = 0; i != stateCount; i++) { double d = Math.abs(elevels[i]-dy); if (d < dist) { dist = d; selectedCoef = i; } } } public void mouseClicked(MouseEvent e) { if (e.getClickCount() == 2 && selectedCoef != -1) enterSelectedState(); } void enterSelectedState() { int i; for (i = 0; i != stateCount; i++) if (selectedCoef != i) magcoef[i] = 0; magcoef[selectedCoef] = 1; cv.repaint(pause); rescaleGraphs(); } public void mouseEntered(MouseEvent e) { } public void mouseExited(MouseEvent e) { if (!dragging) { if (selectedCoef != -1) { selectedCoef = -1; cv.repaint(pause); } if (selectedPState != 0) { selectedPState = 0; cv.repaint(pause); } if (selectedPaneHandle != -1) { selectedPaneHandle = -1; cv.repaint(pause); } } } public void mousePressed(MouseEvent e) { mouseMoved(e); if ((e.getModifiers() & MouseEvent.BUTTON1_MASK) == 0) return; dragging = true; edit(e); } public void mouseReleased(MouseEvent e) { if ((e.getModifiers() & MouseEvent.BUTTON1_MASK) == 0) return; if (mouseChooser.getSelectedIndex() == MOUSE_EDIT && selection == SEL_POTENTIAL) { adjustingStates = false; statesChanged = true; } if (selection == SEL_STATES && alwaysMaxItem.getState()) maximize(); dragging = adjustingWaveFunc = false; cv.repaint(pause); } public void itemStateChanged(ItemEvent e) { if (e.getItemSelectable() == stoppedCheck) { cv.repaint(pause); return; } if (e.getItemSelectable() == setupChooser) doSetup(); if (e.getItemSelectable() instanceof CheckboxMenuItem) { handleResize(); cv.repaint(pause); } if (e.getItemSelectable() == alwaysNormItem && alwaysNormItem.getState()) { normalize(); alwaysMaxItem.setState(false); cv.repaint(pause); } if (e.getItemSelectable() == alwaysMaxItem && alwaysMaxItem.getState()) { maximize(); alwaysNormItem.setState(false); cv.repaint(pause); } int i; for (i = 0; i != waveFunctionMenu.countItems(); i++) if (e.getItemSelectable() == waveFunctionMenu.getItem(i)) { int j; ((CheckboxMenuItem) waveFunctionMenu.getItem(i)) .setState(true); for (j = 0; j != waveFunctionMenu.countItems(); j++) if (i != j) ((CheckboxMenuItem) waveFunctionMenu.getItem(j)) .setState(false); rescaleGraphs(); } } void doSetup() { doBlank(); int i; for (i = 0; i != sampleCount; i++) func[i] = funci[i] = pot[i] = 0; setup = (Setup) setupList.elementAt(setupChooser.getSelectedIndex()); aux1Bar.setValue(100); aux2Bar.setValue(100); aux3Bar.setValue(100); selectGround = true; setup.select(); setup.drawPotential(); setupModified = false; statesChanged = true; if (setup.getAuxBarCount() >= 2) { aux2Label.show(); aux2Bar.show(); } else { aux2Label.hide(); aux2Bar.hide(); } if (setup.getAuxBarCount() == 3) { aux3Label.show(); aux3Bar.show(); } else { aux3Label.hide(); aux3Bar.hide(); } if (setup.allowLeftRight()) leftRightCheckItem.enable(); else { leftRightCheckItem.disable(); leftRightCheckItem.setState(false); } handleResize(); validate(); selectedCoef = -1; } void measureE() { normalize(); double n = random.nextDouble(); int i; for (i = 0; i != stateCount; i++) { double m = magcoef[i]*magcoef[i]; n -= m; if (n < 0) break; } if (i == stateCount) return; int pick = i; for (i = 0; i != stateCount; i++) magcoef[i] = 0; magcoef[pick] = 1; rescaleGraphs(); } void measureX() { int i; double n = random.nextDouble(); for (i = 0; i != sampleCount; i++) { double m = func[i]*func[i] + funci[i]*funci[i]; n -= m; if (n < 0) break; } if (i == sampleCount) return; int pick = i; for (i = 0; i != sampleCount; i++) func[i] = funci[i] = 0; func[pick] = 1; transform(); rescaleGraphs(); normalize(); } class FFT { double wtabf[]; double wtabi[]; int size; FFT(int sz) { size = sz; if ((size & (size-1)) != 0) System.out.println("size must be power of two!"); calcWTable(); } void calcWTable() { // calculate table of powers of w wtabf = new double[size]; wtabi = new double[size]; int i; for (i = 0; i != size; i += 2) { double pi = 3.1415926535; double th = pi*i/size; wtabf[i ] = Math.cos(th); wtabf[i+1] = Math.sin(th); wtabi[i ] = wtabf[i]; wtabi[i+1] = -wtabf[i+1]; } } void transform(double data[], boolean inv) { int i; int j = 0; int size2 = size*2; if ((size & (size-1)) != 0) System.out.println("size must be power of two!"); // bit-reversal double q; int bit; for (i = 0; i != size2; i += 2) { if (i > j) { q = data[i]; data[i] = data[j]; data[j] = q; q = data[i+1]; data[i+1] = data[j+1]; data[j+1] = q; } // increment j by one, from the left side (bit-reversed) bit = size; while ((bit & j) != 0) { j &= ~bit; bit >>= 1; } j |= bit; } // amount to skip through w table int tabskip = size << 1; double wtab[] = (inv) ? wtabi : wtabf; int skip1, skip2, ix, j2; double wr, wi, d1r, d1i, d2r, d2i, d2wr, d2wi; // unroll the first iteration of the main loop for (i = 0; i != size2; i += 4) { d1r = data[i]; d1i = data[i+1]; d2r = data[i+2]; d2i = data[i+3]; data[i ] = d1r+d2r; data[i+1] = d1i+d2i; data[i+2] = d1r-d2r; data[i+3] = d1i-d2i; } tabskip >>= 1; // unroll the second iteration of the main loop int imult = (inv) ? -1 : 1; for (i = 0; i != size2; i += 8) { d1r = data[i]; d1i = data[i+1]; d2r = data[i+4]; d2i = data[i+5]; data[i ] = d1r+d2r; data[i+1] = d1i+d2i; data[i+4] = d1r-d2r; data[i+5] = d1i-d2i; d1r = data[i+2]; d1i = data[i+3]; d2r = data[i+6]*imult; d2i = data[i+7]*imult; data[i+2] = d1r-d2i; data[i+3] = d1i+d2r; data[i+6] = d1r+d2i; data[i+7] = d1i-d2r; } tabskip >>= 1; for (skip1 = 16; skip1 <= size2; skip1 <<= 1) { // skip2 = length of subarrays we are combining // skip1 = length of subarray after combination skip2 = skip1 >> 1; tabskip >>= 1; for (i = 0; i != 1000; i++); // for each subarray for (i = 0; i < size2; i += skip1) { ix = 0; // for each pair of complex numbers (one in each subarray) for (j = i; j != i+skip2; j += 2, ix += tabskip) { wr = wtab[ix]; wi = wtab[ix+1]; d1r = data[j]; d1i = data[j+1]; j2 = j+skip2; d2r = data[j2]; d2i = data[j2+1]; d2wr = d2r*wr - d2i*wi; d2wi = d2r*wi + d2i*wr; data[j] = d1r+d2wr; data[j+1] = d1i+d2wi; data[j2 ] = d1r-d2wr; data[j2+1] = d1i-d2wi; } } } } } abstract class Setup { abstract String getName(); abstract void select(); abstract Setup createNext(); void fudgeLevels() { } boolean allowLeftRight() { return false; } abstract void drawPotential(); int getAuxBarCount() { return 2; } void getInfo(String s[], int offset) { } double getBaseEnergy() { return -1; } }; class InfiniteWellSetup extends Setup { String getName() { return "Infinite Well"; } void select() { aux1Label.setText("Well Width"); } double getBaseEnergy() { return 1; } boolean allowLeftRight() { return !setupModified; } void drawPotential() { int i; int width = getOffset(); for (i = 0; i != sampleCount; i++) pot[i] = infiniteEnergy; for (i = width; i <= sampleCount-1-width; i++) pot[i] = -1; } int getOffset() { return (100-aux1Bar.getValue())*(sampleCount/2)/110+1; } int getAuxBarCount() { return 1; } void fudgeLevels() { // change levels to exact values so that states are periodic int i; for (i = 1; i != stateCount; i++) elevels[i] = (elevels[0]+1)*(i+1)*(i+1)-1; } void getInfo(String s[], int o) { s[o] = "Well width = " + getLengthText(sampleCount-getOffset()*2); } Setup createNext() { return new FiniteWellSetup(); } } class FiniteWellSetup extends Setup { String getName() { return "Finite Well"; } void select() { aux1Label.setText("Well Width"); aux1Bar.setValue(100); aux2Label.setText("Well Depth"); } int getOffset() { return (100-aux1Bar.getValue()*6/10)*(sampleCount/2)/110; } double getFloor() { return 1-(aux2Bar.getValue())/50.; } void drawPotential() { int i; int width = getOffset(); double floor = getFloor(); for (i = 0; i != sampleCount; i++) pot[i] = 1; for (i = width; i <= sampleCount-1-width; i++) pot[i] = floor; } void getInfo(String s[], int o) { s[o] = "Well width = " + getLengthText(sampleCount-getOffset()*2); s[o] += ", Well depth = " + getEnergyText(1-getFloor(), false); } Setup createNext() { return new HarmonicOscillatorSetup(); } } class HarmonicOscillatorSetup extends Setup { String getName() { return "Harmonic Oscillator"; } boolean allowLeftRight() { return !setupModified; } void select() { aux1Label.setText("Spring Constant"); aux1Bar.setValue(0); aux2Label.setText("Offset"); aux2Bar.setValue(50); } double a; void drawPotential() { int i; double width = (sampleCount/2)/(.062333*aux1Bar.getValue()+1.1); int offset = (50-aux2Bar.getValue())*(sampleCount/2)/100; a = 2/(width*width); for (i = 0; i != sampleCount; i++) { int ii = offset+i-sampleCount/2; pot[i] = a*ii*ii-1; } pot[0] = pot[sampleCount-1] = infiniteEnergy; } double getBaseEnergy() { return 1; } void getInfo(String s[], int o) { // convert pixels to meters double p1 = 1/pointsToLength(1); double k = a*2*convertEnergy(1, false)*p1*p1; s[o] = "k = " + getUnitText(k*1e-18, "eV") + "/nm^2"; double f = Math.sqrt(k/(mass/8.988e16))/(2*pi); s[o] += ", period = " + getUnitText(1/f, "s"); } void fudgeLevels() { int i; if (stateCount < 10) return; double avg = 0; for (i = 0; i != 10; i++) avg += elevels[i+1]-elevels[i]; avg /= 10; for (i = 1; i != stateCount; i++) { // if the levels are way off then leave them alone. this // can happen if the offset is too far to the left, for // example. if ((elevels[i]-elevels[i-1])/avg > 2) break; elevels[i] = elevels[i-1]+avg; } } Setup createNext() { return new FiniteWellPairSetup(); } } class FiniteWellPairSetup extends Setup { String getName() { return "Well Pair"; } void select() { aux1Label.setText("Well Width"); aux2Bar.setValue(10); aux2Label.setText("Well Separation"); aux3Label.setText("Well Depth"); } int getAuxBarCount() { return 3; } double getFloor() { return 1-(aux3Bar.getValue())/50.; } int getWidth() { return (aux1Bar.getValue()*3/4)*(sampleCount/2)/110+1; } int getSep() { return (sampleCount/2-getWidth())*aux2Bar.getValue()/150+1; } void drawPotential() { int i; int width = getWidth(); int sep = getSep(); double floor = getFloor(); for (i = 0; i != sampleCount; i++) pot[i] = 1; for (i = 0; i != width; i++) pot[sampleCount/2-i-sep] = pot[sampleCount/2+i+sep] = floor; } void getInfo(String s[], int o) { s[o] = "Well width = " + getLengthText(getWidth()); s[o] += ", Well depth = " + getEnergyText(1-getFloor(), false); s[o+1] = "Well separation = " + getLengthText(getSep()*2); } Setup createNext() { return new FiniteWellPairCoupledSetup(); } } class FiniteWellPairCoupledSetup extends Setup { String getName() { return "Coupled Well Pair"; } void select() { aux1Label.setText("Well Separation"); aux1Bar.setValue(1); aux2Label.setText("Wall Potential"); aux2Bar.setValue(50); } int getWidth() { return sampleCount/4; } int getSep() { return aux1Bar.getValue()*(getWidth()-1)/150+1; } double getWallEnergy() { return -1+(aux2Bar.getValue()-1)/50.; } void drawPotential() { int i; int width = getWidth(); int sep = getSep(); double floor = -1; double infloor = -1+(aux2Bar.getValue()-1)/50.; for (i = 0; i != sampleCount; i++) pot[i] = 1; for (i = 0; i != width; i++) pot[sampleCount/2-i-sep] = pot[sampleCount/2+i+sep] = floor; for (i = 0; i < sep; i++) pot[sampleCount/2-i] = pot[sampleCount/2+i] = infloor; } void getInfo(String s[], int o) { s[o] = "Well width = " + getLengthText(getWidth()); s[o] += ", Well depth = " + getEnergyText(2, false); s[o+1] = "Well separation = " + getLengthText(getSep()*2); s[o+1] += ", Wall potential = " + getEnergyText(getWallEnergy(), true); } Setup createNext() { return new AsymmetricWellSetup(); } } class AsymmetricWellSetup extends Setup { String getName() { return "Asymmetric Well"; } void select() { aux1Label.setText("Width Difference"); aux1Bar.setValue(60); aux2Label.setText("Depth Difference"); aux2Bar.setValue(12); } int w1; double floor2; void getInfo(String s[], int o) { s[o] = "Left well width = " + getLengthText(w1); s[o] += ", energy = " + getEnergyText(-1, true); s[o+1] = "Right well width = " + getLengthText(sampleCount-2-w1); s[o+1] += ", energy = " + getEnergyText(floor2, true); } void drawPotential() { pot[0] = pot[sampleCount-1] = infiniteEnergy; w1 = aux1Bar.getValue()*(sampleCount-2)/100; floor2 = aux2Bar.getValue()*2/100. - 1; int i; for (i = 1; i != w1; i++) pot[i] = -1; for (i = w1; i < sampleCount-1; i++) pot[i] = floor2; } double getBaseEnergy() { return 1; } Setup createNext() { return new InfiniteWellFieldSetup(); } } class InfiniteWellFieldSetup extends Setup { String getName() { return "Infinite Well + Field"; } void select() { aux1Label.setText("Well Width"); aux2Label.setText("Field Strength"); } int width; double field; void getInfo(String s[], int o) { int realwidth = sampleCount - width*2; s[o] = "Well width = " + getLengthText(realwidth); double w = pointsToLength(realwidth); double ed = pot[width]-pot[sampleCount-1-width]; double vd = convertEnergy(ed, false); s[o] += ", voltage difference = " + getUnitText(vd, "V"); s[o+1] = "(Particle charge = electron charge)"; } void drawPotential() { int i; width = (100-aux1Bar.getValue())*(sampleCount/2)/110+1; for (i = 0; i != sampleCount; i++) pot[i] = infiniteEnergy; field = -(aux2Bar.getValue()-50)/(50.*sampleCount/2); for (i = width; i <= sampleCount-1-width; i++) pot[i] = (i-sampleCount/2)*field; } double getBaseEnergy() { return 0; } Setup createNext() { return new WellPairCoupledFieldSetup(); } } class WellPairCoupledFieldSetup extends Setup { String getName() { return "Coupled Wells + Field"; } void select() { aux1Label.setText("Well Separation"); aux1Bar.setValue(1); aux2Label.setText("Field Strength"); } double getBaseEnergy() { return .25; } void drawPotential() { int i; int width = sampleCount/8; int sep = aux1Bar.getValue()*(width-1)/101+1; double floor = -1+getBaseEnergy(); double infloor = 1; for (i = 0; i != sampleCount; i++) pot[i] = infiniteEnergy; double field = -(aux2Bar.getValue()-50)/(100.*sampleCount/2); for (i = 0; i != width; i++) { double q = (i+sep)*field; pot[sampleCount/2-i-sep] = floor+q; pot[sampleCount/2+i+sep] = floor-q; } for (i = 0; i < sep; i++) pot[sampleCount/2-i] = pot[sampleCount/2+i] = infloor; } Setup createNext() { return new CoulombSetup(); } } class CoulombSetup extends Setup { String getName() { return "Coulomb"; } void select() { aux1Label.setText("Charge"); aux1Bar.setValue(8); } void drawPotential() { int i; double width = (aux1Bar.getValue())*(sampleCount/2)/110.; for (i = 0; i != sampleCount; i++) { int ii = i-sampleCount/2; if (ii < 0) ii = -ii; double v = 1-width/ii; if (v < -1) v = -1; pot[i] = v; } pot[0] = pot[sampleCount-1] = infiniteEnergy; } int getAuxBarCount() { return 1; } Setup createNext() { return new QuarticOscillatorSetup(); } } class QuarticOscillatorSetup extends Setup { String getName() { return "Quartic Oscillator"; } void select() { aux1Label.setText("Spring Constant"); aux1Bar.setValue(0); aux2Label.setText("Offset"); aux2Bar.setValue(50); } double a; void drawPotential() { int i; double width = (sampleCount/2)/(.062333*aux1Bar.getValue()+1.1); int offset = (50-aux2Bar.getValue())*(sampleCount/2)/100; a = 2/(width*width*width*width); for (i = 0; i != sampleCount; i++) { int ii = offset+i-sampleCount/2; pot[i] = a*ii*ii*ii*ii-1; } pot[0] = pot[sampleCount-1] = infiniteEnergy; } double getBaseEnergy() { return 1; } Setup createNext() { return new FiniteWellArraySetup(); } } class FiniteWellArraySetup extends Setup { int width; int wellCount; String getName() { return "Well Array (Square)"; } void select() { aux1Label.setText("Well Count"); aux2Label.setText("Well Depth"); aux3Label.setText("Well Width"); } int getAuxBarCount() { return 3; } double getFloor() { return 1-(aux2Bar.getValue())/50.; } void getInfo(String s[], int o) { s[o] = "Well width = " + getLengthText(width); s[o] += ", Well count = " + wellCount; s[o+1] = "Well depth = " + getEnergyText(1-getFloor(), false); } void drawPotential() { int i; int maxWells = 10; if (sampleCount > 260) maxWells = sampleCount/26; int period = (sampleCount*7/(maxWells*8))*(aux3Bar.getValue()+60)/160; int sep = (sampleCount/(maxWells*8)); if (sep == 0) { sep++; period--; } wellCount = aux1Bar.getValue()*(maxWells)/101+1; double floor = getFloor(); int offset = (sampleCount-wellCount*period)/2; width = period-sep; for (i = 0; i != sampleCount; i++) { if (i < offset) pot[i] = 1; else { int ii = i-offset; int j = (ii % period); pot[i] = (j < sep || ii/period >= wellCount) ? 1 : floor; } } } Setup createNext() { return new HarmonicWellArraySetup(); } } class HarmonicWellArraySetup extends FiniteWellArraySetup { String getName() { return "Well Array (Harmonic)"; } void drawPotential() { int i; int maxWells = 5; if (sampleCount > 260) maxWells = sampleCount/52; int period = (sampleCount*7/(maxWells*8))*(aux3Bar.getValue()+60)/160; int sep = (sampleCount/(maxWells*8)); if (sep == 0) { sep++; period--; } wellCount = aux1Bar.getValue()*(maxWells)/101+1; double floor = getFloor(); int offset = (sampleCount-wellCount*period)/2; width = period-sep; double a = (1-floor)/((width/2)*(width/2.)); for (i = 0; i != sampleCount; i++) { if (i < offset) pot[i] = 1; else { int ii = i-offset; int j = (ii % period); if (j < sep || ii/period >= wellCount) pot[i] = 1; else { double xx = (j-sep-width/2.); pot[i] = floor+xx*xx*a; if (pot[i] > 1) pot[i] = 1; } } } } Setup createNext() { return new CoulombWellArraySetup(); } } class CoulombWellArraySetup extends FiniteWellArraySetup { String getName() { return "Well Array (Coulomb)"; } void select() { super.select(); aux2Bar.setValue(48); } void getInfo(String s[], int o) { s[o] = "Well width = " + getLengthText(width); s[o] += ", Well count = " + wellCount; s[o+1] = "Well depth = " + getEnergyText(2, false); } void drawPotential() { int i; int maxWells = 5; if (sampleCount > 260) maxWells = sampleCount/52; int period = (sampleCount*7/(maxWells*8))*(aux3Bar.getValue()+60)/160; int sep = (sampleCount/(maxWells*8)); if (sep == 0) { sep++; period--; } wellCount = aux1Bar.getValue()*(maxWells)/101+1; double s = (aux2Bar.getValue())/400.; int offset = (sampleCount-wellCount*period)/2; width = period-sep; s *= width/2; double a = -2*width*s/(2*s-width); double b = 1+2*a/width; for (i = 0; i != sampleCount; i++) { if (i < offset) pot[i] = 1; else { int ii = i-offset; int j = (ii % period); if (j < sep || ii/period >= wellCount) pot[i] = 1; else { double xx = (j-sep-width/2.); pot[i] = b-a/Math.abs(xx); if (pot[i] < -1) pot[i] = -1; } } } } Setup createNext() { return new FiniteWellArrayFieldSetup(); } } class FiniteWellArrayFieldSetup extends Setup { int width; int wellCount; String getName() { return "Well Array + Field"; } void select() { aux1Label.setText("Well Count"); aux2Label.setText("Well Width"); aux3Label.setText("Field Strength"); aux3Bar.setValue(90); if (massBar.getValue() == 16 && resBar.getValue() <= 260) { // set up interesting case (bloch oscillation) selectGround = false; magcoef[3] = .067; magcoef[4] = .2629; magcoef[5] = .6771; magcoef[6] = 1; magcoef[7] = .586156; magcoef[8] = .1058; magcoef[9] = .078; int i; for (i = 0; i != stateCount; i++) phasecoefadj[i] = (i == 6) ? 0 : pi; } } int getAuxBarCount() { return 3; } void getInfo(String s[], int o) { } void drawPotential() { int i; int maxWells = 10; if (sampleCount > 260) maxWells = sampleCount/26; int period = (sampleCount*7/(maxWells*8))*(aux2Bar.getValue()+60)/160; int sep = (sampleCount/(maxWells*8)); if (sep == 0) { sep++; period--; } double field = -(aux3Bar.getValue()-50)/(200.*sampleCount/2); wellCount = aux1Bar.getValue()*(maxWells)/101+1; double floor = -.75; int offset = (sampleCount-wellCount*period)/2; width = period-sep; for (i = 0; i != sampleCount; i++) { if (i < offset) pot[i] = .75; else { int ii = i-offset; int j = (ii % period); pot[i] = (j < sep || ii/period >= wellCount) ? .75 : floor; } pot[i] += (i-sampleCount/2)*field; } pot[0] = pot[sampleCount-1] = infiniteEnergy; } Setup createNext() { return new FiniteWellArrayImpureSetup(); } } class FiniteWellArrayImpureSetup extends FiniteWellArraySetup { String getName() { return "Well Array w/ Impurity"; } void select() { aux1Label.setText("Impurity Position"); aux2Label.setText("Well Depth"); aux3Label.setText("Impurity Depth"); aux1Bar.setValue(75); aux3Bar.setValue(85); } void getInfo(String s[], int o) {} void drawPotential() { int i; int maxWells = 10; if (sampleCount > 260) maxWells = sampleCount/26; int period = (sampleCount*7/(maxWells*8)); int sep = (sampleCount/(maxWells*8)); if (sep == 0) { sep++; period--; } wellCount = maxWells; double floor = 1-(aux2Bar.getValue())/50.; double impfloor = 1-(aux3Bar.getValue())/50.; int pos = aux1Bar.getValue()*maxWells/101; int offset = (sampleCount-wellCount*period)/2; width = period-sep; for (i = 0; i != sampleCount; i++) { if (i < offset) pot[i] = 1; else { int ii = i-offset; int j = (ii % period); double f = (ii/period == pos) ? impfloor : floor; pot[i] = (j < sep || ii/period >= wellCount) ? 1 : f; } } } double getFloor() { return -1; } Setup createNext() { return new FiniteWellArrayDislocSetup(); } } class FiniteWellArrayDislocSetup extends FiniteWellArraySetup { String getName() { return "Well Array w/ Dislocation"; } void select() { aux1Label.setText("Impurity Position"); aux1Bar.setValue(75); aux2Label.setText("Well Depth"); aux3Label.setText("Impurity Offset"); aux3Bar.setValue(80); } void getInfo(String s[], int o) {} void drawPotential() { int i; int maxWells = 8; int period = (sampleCount*7/(maxWells*8)); int sep = (sampleCount/(maxWells*4)); if (sep == 0) { sep++; period--; } wellCount = maxWells; double floor = 1-(aux2Bar.getValue())/50.; int pos = aux1Bar.getValue()*maxWells/101; int offset = (sampleCount-wellCount*period)/2; int ioffset = (50-aux3Bar.getValue())*(sep-1)/50; width = period-sep; for (i = 0; i != sampleCount; i++) { if (i < offset) pot[i] = 1; else { int ii = i-offset; int j = (ii % period); pot[i] = (j < sep || ii/period == pos || ii/period >= wellCount) ? 1 : floor; ii += ioffset; j = (ii % period); if (ii/period == pos && j >= sep) pot[i] = floor; } } } double getFloor() { return -1; } Setup createNext() { return new RandomWellArraySetup(); } } class RandomWellArraySetup extends FiniteWellArraySetup { String getName() { return "Random Well Array"; } void select() { aux1Label.setText("Randomness"); } void getInfo(String s[], int o) {} int getAuxBarCount() { return 1; } void drawPotential() { int i; for (i = 0; i != 10; i++) pot[i] = 1; int ww = 8; while (i < sampleCount-(15+ww)) { int j; for (j = 0; j != ww; j++) pot[i++] = -1; int sep = 8+((getrand(15)-7) * aux1Bar.getValue()/100); for (j = 0; j != sep; j++) pot[i++] = 1; } for (; i != sampleCount; i++) pot[i] = 1; } Setup createNext() { return new FiniteWell2ArraySetup(); } } class FiniteWell2ArraySetup extends Setup { int width; int wellCount; String getName() { return "2 Well Array"; } void select() { aux1Label.setText("Well Count"); aux2Label.setText("Well Depth"); aux3Label.setText("Well Width"); } int getAuxBarCount() { return 3; } double getFloor() { return 1-(aux2Bar.getValue())/50.; } void getInfo(String s[], int o) {} void drawPotential() { int i; int maxWells = 10; if (sampleCount > 260) maxWells = sampleCount/26; maxWells |= 1; int period = (sampleCount*7/(maxWells*8))*(aux3Bar.getValue()+60)/160; int sep = (sampleCount/(maxWells*8)); if (sep == 0) { sep++; period--; } wellCount = aux1Bar.getValue()*(maxWells)/101+1; double floor = getFloor(); int offset = (sampleCount-wellCount*period)/2; width = period-sep; for (i = 0; i != sampleCount; i++) { if (i < offset) pot[i] = 1; else { int ii = i-offset; int j = (ii % period); double f = (ii/period % 2 == 0) ? floor : -.5; pot[i] = (j < sep || ii/period >= wellCount) ? 1 : f; } } } Setup createNext() { return new FiniteWellCoupledArraySetup(); } } class FiniteWellCoupledArraySetup extends Setup { int width; int wellCount; String getName() { return "Coupled Well Array"; } void select() { aux1Label.setText("Well Count"); aux2Label.setText("Wall Potential"); aux2Bar.setValue(50); } int getAuxBarCount() { return 2; } double getWallPot() { return 1-(aux2Bar.getValue())/50.; } void getInfo(String s[], int o) {} void drawPotential() { int i; int maxWells = 10; if (sampleCount > 260) maxWells = sampleCount/26; maxWells |= 1; int period = (sampleCount*7/(maxWells*8)); int sep = (sampleCount/(maxWells*8)); if (sep == 0) { sep++; period--; } wellCount = aux1Bar.getValue()*(maxWells)/102+2; wellCount &= ~1; // must be even int offset = (sampleCount-wellCount*period)/2; width = period-sep; for (i = 0; i != sampleCount; i++) { if (i < offset || i > sampleCount-offset) pot[i] = 1; else { int ii = i-offset; int j = (ii % period); double wall = (ii/period % 2 == 0) ? 1 : getWallPot(); pot[i] = (j < sep || ii/period >= wellCount) ? wall : -1; } } } Setup createNext() { return new DeltaArraySetup(); } } /*class SinusoidalLatticeSetup extends Setup { String getName() { return "Sinusoidal Lattice"; } void select() { aux1Label.setText("Well Count"); aux2Label.setText("Well Depth"); } int getAuxBarCount() { return 2; } void drawPotential() { int n = aux1Bar.getValue() / 10; double amp = aux2Bar.getValue()/100.; int buf = sampleCount/10; int i; for (i = 0; i != sampleCount; i++) pot[i] = 1; for (i = buf; i != sampleCount-buf; i++) { double xx = (i-buf)/(sampleCount-buf*2.); pot[i] = 1-amp*(1-Math.cos(xx*2*pi*n)); } } Setup createNext() { return new DeltaArraySetup(); } }*/ class DeltaArraySetup extends Setup { String getName() { return "Delta Fn Array"; } void select() { aux1Label.setText("Well Count"); aux1Bar.setValue(32); aux2Label.setText("Well Separation"); aux2Bar.setValue(30); } void drawPotential() { int i; int maxWells = 30; int width = aux2Bar.getValue()/5+2; int count = aux1Bar.getValue()*(maxWells)/101+1; int offset = (sampleCount-(count-1)*width+1)/2; for (i = 1; i != sampleCount; i++) { if (i < offset) pot[i] = 1; else { int ii = i-offset; int j = (ii % width); pot[i] = 1; if (j == 0 && count-- > 0) pot[i] = -1; } } for (i = 0; i != width; i++) pot[i] = pot[sampleCount-1-i] = 1; } Setup createNext() { return null; } } class View extends Rectangle { int mid_y, lower_y; double ymult, ymult2, scale; } }; interface DecentScrollbarListener { abstract void scrollbarValueChanged(DecentScrollbar ds); abstract void scrollbarFinished(DecentScrollbar dc); } // this is a scrollbar that notifies us when the user is _done_ fiddling // with the value. class DecentScrollbar extends Canvas implements MouseListener, MouseMotionListener { int value, lo, hi; DecentScrollbarListener listener; DecentScrollbar(DecentScrollbarListener parent, int start, int lo_, int hi_) { value = start; lo = lo_; hi = hi_; listener = parent; addMouseListener(this); addMouseMotionListener(this); gray1 = new Color(104, 104, 104); gray2 = new Color(168, 168, 168); gray3 = new Color(192, 192, 192); gray4 = new Color(224, 224, 224); } Color gray1, gray2, gray3, gray4; public Dimension getPreferredSize() { return new Dimension(20,20); } static final int tw = 8; boolean dragging; int thumbpos, dragoffset; public void paint(Graphics g) { Dimension size = getSize(); int w = size.width; int h = size.height; int x = thumbpos = (value-lo)*(w-2-tw)/(hi-lo)+1; g.setColor(gray2); g.fillRect(0, 0, w, h); g.setColor(gray3); g.fillRect(x, 2, tw, h-4); g.setColor(gray4); g.drawLine(0, h-1, w, h-1); g.drawLine(w-1, 1, w-1, h-1); g.drawLine(x, 1, x+tw-1, 1); g.drawLine(x, 1, x, h-2); g.setColor(gray1); g.drawLine(0, 0, w-1, 0); g.drawLine(0, 0, 0, h-1); g.drawLine(x+tw-1, 2, x+tw-1, h-2); g.drawLine(x+1, h-2, x+tw-1, h-2); } int getValue() { return value; } boolean setValue(int v) { if (v < lo) v = lo; if (v > hi) v = hi; if (value == v) return false; value = v; repaint(); return true; } public void mousePressed(MouseEvent e) { if (thumbpos <= e.getX() && thumbpos+tw >= e.getX()) { dragging = true; dragoffset = e.getX()-thumbpos; } } public void mouseReleased(MouseEvent e) { if (dragging) listener.scrollbarFinished(this); dragging = false; } public void mouseClicked(MouseEvent e) { } public void mouseEntered(MouseEvent e) { } public void mouseExited(MouseEvent e) { } public void mouseDragged(MouseEvent e) { if (!dragging) return; int x = e.getX()-dragoffset; Dimension size = getSize(); int v = (x-1)*(hi-lo)/(size.width-2-tw)+lo; if (setValue(v)) listener.scrollbarValueChanged(this); } public void mouseMoved(MouseEvent e) { } };