HOmovSlow.py

""" From "COMPUTATIONAL PHYSICS" & "COMPUTER RhoLEMS in PHYSICS"
    by RH Landau, MJ Paez, and CC Bordeianu (deceased)
    Copyright R Landau, Oregon State Unv, MJ Paez, Univ Antioquia, 
    C Bordeianu, Univ Bucharest, 2017. 
    Please respect copyright & acknowledge our work."""

# HOmovieSlow.py: Solves & animates S Eq for wavepacket in HO    

from visual import *   
         # initialize wave function, Rhoability, potential (2m=1)
xmax = 300;  dx = 0.04;  dx2 = dx*dx;  k0 = 5.5*math.pi
dt = dx2/4.; xp = -6;  Rho = zeros((xmax+1),float)
V = zeros((xmax+1), float)
RePsi = zeros((xmax+1,2), float);  ImPsi = zeros((xmax+1,2), float)                                 
g = display(width = 500, height = 250,
	title = 'Wave Packet Harmonic Well')
PlotObj =  curve(x = range(0, 300+1), color = color.yellow)           
for i in range(0, xmax):                       # Initialize  
   xp2      = xp * xp
   RePsi[i,0] = math.exp(-0.5*xp2/0.25) * math.cos(k0*xp);       
   ImPsi[i,0] = math.exp(-0.5*xp2/0.25) * math.sin(k0*xp);       
   V[i]     = 15.0*xp2                                                
   xp      += dx
   count    = 0
while 1:                        # RePsi time propagation
   for i in range(1, xmax - 1):                                
       RePsi[i,1] = RePsi[i,0]-dt*(ImPsi[i+1,0] + ImPsi[i-1,0]
                     -2.*ImPsi[i,0])/(dx2) + dt*V[i]*ImPsi[i,0]
       Rho[i] = RePsi[i,0]*RePsi[i,1] + ImPsi[i,0]*ImPsi[i, 0]
   if count %10 == 0:               # Add points to plot
       j = 0
       for i in range(1, xmax-1, 3):         
            PlotObj.x[j] = 2*i - xmax
            PlotObj.y[j] = 130*Rho[i]
            j = j + 1
       PlotObj.radius = 4.0 
       PlotObj.pos                              # Add points
   for i in range(1, xmax - 1):
        ImPsi[i,1] = ImPsi[i,0] + dt*(RePsi[i+1,1] + RePsi[i-1,1]
                    -2.*RePsi[i,1])/dx2 - dt*V[i]*RePsi[i,1]
   for  i in range(0, xmax):
       ImPsi[i,0] = ImPsi[i,1]
       RePsi[i,0] = RePsi[i][1] 
   count  =  count + 1