/* This code solves the Schroedinger equation for a wavepacket
   incident on a square potential barrier. The solution method is
   the simple Euler's method. This can be improved with, e.g., a
   Cranck-Nickolson method. But, it is good enough for teaching
   purposes.
   For the HTML code use:
   <applet code= Potbar.class width=650 height=400> </applet>
   C.A. Bertulani, 08/23/2000
*/
import java.awt.*;
import java.applet.*;
import java.awt.image.*;
public class Potbar extends Applet implements Runnable {
  Thread runstring;
  // Creates a scrollbar with the specified orientation, value, extent, 
  // mimimum, and maximum: value = initial position of scroll, extent =
  // width of scroll, minimum = minimun pixel number associated with position
  public Scrollbar leftRight;
  // A Canvas represents a blank rectangular area of the screen 
  // onto which the application can draw or from which the application can 
  // trap input events from the user. 
  private MyCanvas canv;
  // A panel provides space in which an application can attach any other 
  // component, including other panels. 
  private MyPanel thePanel;
  // A border layout lays out a container, arranging and resizing its 
  // components to fit in five regions: north, south, east, west, and center.   
  BorderLayout MyLay;
  // global variables
  int Flag;
  public boolean stopped = false;

  public Potbar() // to initialize Flag
  {
     setFlag(0);
  }

  public void setFlag(int fl)
  {
     Flag = fl;    // Flag 0 do not begin string motion, 1 yes
   }
  public void init()
  {
    setLayout(MyLay = new BorderLayout());
    thePanel = new MyPanel(this,canv);
    leftRight = new Scrollbar(Scrollbar.HORIZONTAL,40,0,10,110);
    canv = new MyCanvas(this);
    canv.init();
    thePanel.init();
    add("Center",canv); // centering Canvas
    add("North",leftRight); // scrollbar at the top
    add("South", thePanel); // panel at the bottom
  }
  public void start()
  {
    if(! stopped)
    {
    if(Flag == 1){
       canv.jj = 1;  // initial condition
       canv.flag = 1;
       runstring = new Thread(this);
       runstring.start();
     }
    }
  }
  public void stop()
  {
     if(runstring != null){
        runstring = null;
     }
  }
  public void brk()  //stops motion temporarily
  {   
      stopped = false;
      setFlag(0);
      canv.jj = 1;   // back to initial condition
  }

  public void run()
  {
    while(true){     
      try{
		  // during 380 miliseconds the thread does not run, even if the 
		  // processor becomes available.
        Thread.currentThread().sleep(380);}
      catch
          (InterruptedException e){ }
            canv.repaint();  // update of the applet's display area
    }
  }

  public void paint(Graphics g){
     canv.repaint();    //called many times
  }
  public boolean handleEvent(Event ev){
  // events sent by Mypanel and scrollbar interpreted here
  // scrollbar movements
  if(ev.target instanceof Scrollbar){
    if(ev.target == leftRight)canv.setWidth(leftRight.getValue());
    canv.repaint();
    return true;
  }
  // mouse movements
  if((ev.id==ev.MOUSE_DRAG)){
       canv.Xmos=ev.x;
       canv.Ymos=ev.y;
       canv.erase=true;
	   // requests that the argument string be displayed in the "status window". 
       showStatus("Cursor at position x = " + ev.x + " and y = " + ev.y);
       canv.repaint();
       return true;
  }
    if(ev.id==ev.MOUSE_ENTER){
    //to show black square at beginning
    //when mouse enters the applet
     canv.repaint();
     return true;
   }
    return false;
 }
} //class

class MyCanvas extends Canvas implements ImageObserver{
   // all the painting occurs here
   Potbar runstring;  // run thread
   int ixmesh0, ixmeshN; 
   double y0, yN;
   double myp,mxp,byp,bxp;
   double Stretchxx,Coefxx,Stretchyy,Coefyy,yypos,xxpos,pi,dx,dt;
   private Image offScreenImage;  // to avoid flicker
   Graphics offScreenGraphics;
   int ypos,xpos,max,cor;
   int Xmos,Ymos,Xdef,Ydef; //mouse positions
   boolean erase=false;
   int first,incr,jj = 1;  // jj=1 is for initial conditions
   int AppletHeight, AppletWidth, xleft,yupper,xsize,ysize;
   double margin;
 
   double  psr[][], psi[][], v[], p2[];
   int flag = 0; //do not draw equation
   
   public void init()
   {
     y0=0.0;
     yN=1.5;
     ixmesh0=0;
     ixmeshN=500;
     max=ixmeshN-ixmesh0;
     Dimension d = getSize(); 
     AppletHeight = d.height; 
     AppletWidth  = d.width;
     margin = 0.1;  // percent used in margin
     xleft = (int)(margin*AppletWidth); // x pixel-left point
     yupper = (int)(margin*AppletHeight); // y pixel-upper point
     xsize = (int)((AppletWidth-2.0*xleft));
     ysize = (int)((AppletHeight-2.0*yupper));
     psr=new double[max+1][2];
     psi=new double[max+1][2];
     p2=new double[max+1];
     v=new double[max+1];
     jj = 1;
     pi=3.14159265358979323846;
     dx=0.02;   // coordinate-x step
     dt=0.9*dx*dx;   // convenient time step size
     incr=10;
     cor=20;
 }

   public MyCanvas(Potbar runstring) //to initialize class and variables
   {
     this.runstring=runstring;
     setWidth(50);  //initial position of the horizontal
   }
  public void update(Graphics g)
  { //To avoid screen flicker use double buffer technique
    Dimension d = getSize(); 
    AppletHeight = d.height; 
    AppletWidth  = d.width;
	// copy image of screen
	offScreenImage=createImage(AppletWidth,AppletHeight);
    offScreenGraphics=offScreenImage.getGraphics();
    offScreenGraphics.setColor(getBackground());
    offScreenGraphics.fillRect(0,0,AppletWidth,AppletHeight);
    offScreenGraphics.setColor(g.getColor());
    paint(offScreenGraphics);  // paint image
    g.drawImage(offScreenImage,0,0,this);  // 0,0 is the image x,y position
  }
  public void setWidth(int hx)
   {
     xpos=hx;
   }
    
  void CoordUndo(double ixmesh0,double ixmeshN,double y0,double yN)
  {  // changes x-mesh-indexing and y-coordinate definition into
     // java applet coordinate system of pixels	
	// put graph within a margin from applet window
    double xxmax = (1.0-margin)*AppletWidth; // right x-pixel-limit  
    double xxmin = margin*AppletWidth; // left x-pixel-limit
    double yymin = (1.0-margin)*AppletHeight; // upper y-pixel-limit
    double yymax = margin*AppletHeight; // lower y-pixel-limit
	// fit data within graph axis 
	// first transform mesh indices into x-window-pixel coordinates
    Stretchxx = (xxmax-xxmin)/(ixmeshN-ixmesh0);
    Coefxx = (xxmin*ixmeshN-xxmax*ixmesh0)/(ixmeshN-ixmesh0);
	// now transform graph y-values to y-window-pixel coordinates
    Stretchyy = (yymax-yymin)/(yN-y0);
    Coefyy = (yymin*yN-yymax*y0)/(yN-y0);
  }
   
  private int pixx(int ivalue)  { 
    // Given the  index of the mesh-xpoint return the pixel equivalent 
    int jvalue = (int)(Stretchxx*ivalue + Coefxx);
    return jvalue; 
  }  

  private int pixy(double yvalue)  { 
    // Given the y-value in desired scale, return the pixel equivalent 
	int jvalue = (int)(Stretchyy*yvalue + Coefyy);
    return jvalue; 
  }  
 
  public void rectangulo(Graphics g)
  {  //draws instruction rectangle
	 int Rectx =  (int)(xleft+xsize/3.0);
	 int Recty = (int)(yupper+ysize/2.0);
	 int RectW = (int)(xsize/3.0); 
	 int RectH = (int)(ysize/2.0)-2; 
     g.drawRect(Rectx,Recty,RectW,RectH);
	 int xstep = (int)(xsize/10.0);
	 int ystep = (int)(ysize/20.0);
     Xdef = Rectx; 
	 Ydef = Recty;
     g.drawString("Drag mouse",xleft+4*xstep,yupper+13*ystep);
     g.drawString("in this area",xleft+4*xstep,yupper+14*ystep);
     g.drawString("to select potential",xleft+4*xstep,yupper+15*ystep);
  }
  public void inirec(Graphics g)
  {  //initial rectangle
     g.drawOval(Xdef+xsize/3-cor,Ydef+cor,10,10);
     g.drawLine(Xdef+cor,yupper+ysize-2,Xdef+cor,Ydef+cor); // vertical 1
     g.drawLine(Xdef+xsize/3-cor,yupper+ysize-2,Xdef+xsize/3-cor,Ydef+cor);
     g.drawLine(Xdef+cor,Ydef+cor,Xdef+xsize/3-cor,Ydef+cor);  // horizontal
  }

  public void inipot(Graphics g)
  {  //initial potential shown
     g.setColor(Color.black);
     rectangulo(g);
     g.setColor(Color.blue);
     if(erase==false){
       inirec(g);
     }
     else {
       g.setColor(getBackground());
       inirec(g);
     }
     g.setColor(Color.blue);
  }
  
  public void potbar(Graphics g)
  { //selects potential as mouse drags
     if((Xmos<Xdef+xsize/3)&&(Xmos>Xdef)
		&&(Ymos<yupper+ysize-2)&&(Ymos>Ydef)){
       g.drawLine(Xdef+cor,Ymos,Xmos,Ymos);
       g.drawLine(Xdef+cor,yupper+ysize-2,Xdef+cor,Ymos);
       g.drawLine(Xmos,yupper+ysize-2,Xmos,Ymos);
     }
  }
  
 public void selectmom(Graphics g)
 {  //select wave packet momentum with scrollbar and draw frame
   int i;
   // put graph within a margin from applet window
   xleft = (int)(margin*AppletWidth); // x pixel-left point
   yupper = (int)(margin*AppletHeight); // y pixel-upper point
   xsize = (int)((AppletWidth-2.0*xleft));
   ysize = (int)((AppletHeight-2.0*yupper));
   // draw label of scrollbar
   g.drawString("Use scrollbar to Select Wave Packet Momentum ",
				xleft,yupper/2);
   g.setColor(Color.red);
   // draw frame
   g.drawRect(xleft,yupper,xsize,ysize);
   // draw ticks and labels
   for(i=0; i<6; i++){
	 int xincr = (int)(xsize/5);  
	 int tick = xleft+xincr*i;
     int dtick = AppletHeight/50;
     g.drawLine(tick,yupper,tick,yupper+10);
     g.drawString(Integer.toString(-10+4*i),tick,yupper-5);
   }
   for(i=0;i<6;i++){
	 int yincr = (int)(ysize/5);  
	 int tick = yupper+yincr*i;
     int dtick = AppletHeight/50;
     g.drawLine(xleft+xsize-10,tick,xleft+xsize,tick);
     g.drawString(Double.toString((5.-i)/5.),xleft+xsize+5,tick+10);
   }
 }

 public void Equation1(Graphics g)
 { //to draw initial potential wavefunction
   //at beginning and after each stop
   double x,fact2;
   double k0,vh;
   double expon,poten;
   int minix,maxix;
   int i,n,arrow;
   xxpos = (double)xpos;
   x = 0.0;
   minix=0;// initialize
   selectmom(g);
   g.setColor(Color.blue);
   if(jj == 1){
     // initial conditions
	 CoordUndo(ixmesh0,ixmeshN,y0,yN); // transform pixels to coordinates
     inipot(g);
     xxpos=(double)xpos;
     k0=pi*xxpos/10.0;
     arrow=(int)(1.5*xxpos);
     g.setColor(Color.red);
     g.drawLine(xleft+xsize/2-arrow,yupper+ysize/3,xleft+xsize/2,yupper+ysize/3);//arrow
     g.drawLine(xleft+xsize/2-5,yupper+ysize/3-5,xleft+xsize/2,yupper+ysize/3); //upper tip
     g.drawLine(xleft+xsize/2-5,yupper+ysize/3+5,xleft+xsize/2,yupper+ysize/3); //lower tip
     g.setColor(Color.blue);
     potbar(g);
     if(Ymos == 0)Ymos = yupper+ysize/2;
     if(Xmos == 0)Xmos=Xdef+(int)(xsize/3.0);
	 minix = Xdef;
	 poten = AppletHeight/2;
	 maxix = Xmos;
	 if(AppletWidth>0)
	 {
		 minix = (int)(Xdef*(ixmeshN-ixmesh0)/AppletWidth);
		 poten = (double)(AppletHeight-Ymos-yupper);
		 maxix = (int)(Xmos*(ixmeshN-ixmesh0)/AppletWidth);
	 }
     vh = poten;
	 g.drawLine(xleft,yupper+ysize-3,xleft+xsize,yupper+ysize-2); //base line	 
     for(i=0; i<max+1; i++){
       if((i>minix)&&(i<maxix))v[i]=vh;
       else v[i]=0.0;
     }
     for(i=0;i<(int)(max/2)-70;i++){
       //real part of the initial wave function at t=0
       fact2 = 4.0*(x-2.7);
       expon = Math.exp(-fact2*fact2);
       psr[i][0] = (Math.cos(k0*x))*expon;
       //imaginary part of the initial wave function at t=0
       psi[i][0] = (Math.sin(k0*x))*expon;
       x = x+dx;
     }
   }//if jj
   // solution for new times
   for( n=first-1; n<jj+1; n++){
     //real part of wavefunction and probability
     for( i=1;i<(int)max/2-70;i++){
       psr[i][1] = psr[i][0] - dt*(psi[i+1][0] + psi[i-1][0]
                -2.0*psi[i][0])/(2.0*dx*dx)+dt*v[i]*psi[i][0];
       p2[i] = psr[i][0]*psr[i][1]+psi[i][0]*psi[i][0];
     }
     // the probability plotted at times=incr
     if(n == jj){
       for(i=1;i<(int)max/2-70;i++){
         if(i>0){
			// transform coordinates to pixel coordinates			 
			int pixx1=pixx(i-1);
			int pixx2=pixx(i);
			int pixy1=pixy(p2[i-1]/1.5);
			int pixy2=pixy(p2[i]/1.5);
			// draw probabilities
            g.drawLine(pixx1,pixy1,pixx2,pixy2);
			int pixy1v=pixy((v[i-1])*yN/AppletHeight);
			int pixy2v=pixy((v[i])*yN/AppletHeight);
            if(v[i] !=v[i-1])pixx1=pixx2;
            if(n !=1) g.drawLine(pixx1,pixy1v,pixx2,pixy2v);
          }
       }
     }
   }
 }
  public void Equation(Graphics g)
 {
   double x,fact2;
   double k0,vh;
   double expon,poten;
   int i,n,arrow;
   x=0.0;
   selectmom(g);
   g.setColor(Color.blue);
   if(jj == 1){
     // initial conditions
     CoordUndo(ixmesh0,ixmeshN,y0,yN); // transform pixels to coordinates
     xxpos=(double)xpos;
     k0=pi*xxpos/10.0;   // momentum
     g.setColor(Color.blue);
     for(i=0;i<max+1;i++){
       //real part of the initial wave function at t=0
       fact2=4.0*(x-2.7);
       expon=Math.exp(-fact2*fact2);
       psr[i][0] = (Math.cos(k0*x))*expon;
       //imaginary part of the initial wave function at t=0
       psi[i][0] = (Math.sin(k0*x))*expon;
       x=x+dx;
     }
   }//if jj
   // solution for new times
   for( n=first-1; n<jj+1; n++){
     //real part of wavefunction and probability
     for( i=1;i<max;i++){
       psr[i][1]=psr[i][0] - dt*(psi[i+1][0] + psi[i-1][0]
                -2.0*psi[i][0])/(2.0*dx*dx)+dt*v[i]*psi[i][0];
       p2[i]=psr[i][0]*psr[i][1]+psi[i][0]*psi[i][0];
     }
     //imaginary part of the wave function
     for(i=1;i<max;i++){
       psi[i][1] = psi[i][0]+dt*(psr[i+1][1] + psr[i-1][1]
                     -2.0*psr[i][1])/(2.0*dx*dx)-dt*v[i]*psr[i][1];
     }
     // the probability plotted at times=incr
     if(n == jj){
       for(i=1;i<max+1;i++){
         if(i>0){
			// transform coordinates to pixel coordinates			 
			int pixx1=pixx(i-1);
			int pixx2=pixx(i);
			int pixy1=pixy(p2[i-1]/1.5);
			int pixy2=pixy(p2[i]/1.5);
			// draw probabilities
            g.drawLine(pixx1,pixy1,pixx2,pixy2);
			int pixy1v=pixy((v[i-1])*yN/AppletHeight);
			int pixy2v=pixy((v[i])*yN/AppletHeight);
            if(v[i] !=v[i-1])pixx1=pixx2;
            if(n !=1)g.drawLine(pixx1,pixy1v,pixx2,pixy2v);
          }
       }
     }
         // new iterations are now the old ones
     for(i=1;i<max+1;i++){
       psi[i][0]=psi[i][1];
       psr[i][0]=psr[i][1];
     }
   }
 }
  public void paint(Graphics g){
     first = jj;
     if(jj == 1){
       Equation1(g);
     }
     if((runstring.Flag == 1)&&( flag == 1)){
       if(first==incr+1)first = 1;
       if(first >= incr+1)first = jj-incr;
       Equation(g);
       jj = jj+incr;
     }
   }
 }
 class MyPanel extends Panel{
  //controls Stop, start and scrollbars
  //transmits to Eqstring the events
  Potbar runstring;
  // GridBagLayout is a layout manager that aligns components vertically and 
  // horizontally, without requiring that the components be of the same size. 
  GridBagLayout GBLay;
  // GridBagConstraints specifies constraints for components that are laid 
  // out using the GridBagLayout class. 
  GridBagConstraints c;
  MyCanvas canv;

  public void init(){
    GBLay = new GridBagLayout();
    c = new GridBagConstraints();
    setLayout(GBLay);
    c.gridx = 1;
    c.gridy = 1;
    c.gridheight = 1;
	// BOTH resizes the component both horizontally and vertically
    c.fill = GridBagConstraints.BOTH; 
    Button stp = new Button("Stop");
    GBLay.setConstraints(stp,c);
    add(stp);
    c.gridx = 2;
    Button rest = new Button("Start");
    GBLay.setConstraints(rest,c);
    add(rest);
  }
  public MyPanel(Potbar runstring, MyCanvas canv)
  {
    this.canv = canv;
    this.runstring = runstring;
  }

 public boolean action(Event ev, Object arg)
 {
   if (ev.target  instanceof Button) {
     String label = (String)ev.arg;
     if (label.equals("Stop")){
       runstring.brk();
     }
     if(label.equals("Start")){
       runstring.setFlag(1);
       runstring.stopped=false;
       runstring.start();
     }
     return true;
   }
   //else
    if(ev.target instanceof Scrollbar){
      runstring.postEvent(ev);//sent to Eqstring handlEvent
      return true;
    }
    if((ev.id==ev.MOUSE_DRAG)){
      runstring.postEvent(ev);
    }
    return false;
  }
}