!     From: "COMPUTATIONAL PHYSICS 2nd Ed" 
! 		by RH Landau, MJ Paez, and CC Bordeianu 
! 		Copyright Wiley - VCH, 2007.
! 		Electronic Materials copyright: R Landau, Oregon State Univ, 2007;
! 		MJ Paez, Univ Antioquia, 2007; and CC Bordeianu, Univ Bucharest, 2007.
! 		Supported by the US National Science Foundation				 
! 			
! 	  slit.f90: Solves time - dependent Schroedinger equation for a	
! 	  two - dimensional Gaussian wavepacket entering a slit

Program slit

  Implicit none
	Real*8 :: psr(91, 91, 2), psi(91, 91, 2), v(91, 91), p2(91, 91)
	Real*8 :: a1, a2, dt, dx, k0x, k0y, x0, y0, x, y
	Integer i, j, k, max, n, time 
	Complex exc, zi		
	
                   ! input positive int proportional to time for plot
	write(*, *)'Enter a positive Integer from 1(initial time)'
	write(*, *)'to 800 to get wave packet position at that time'
	read(*, *)time
	write(*, *)'processing data for time', time
	open(9, FILE = 'slit.dat', Status = 'Unknown')
                               ! initialize constants and wave packet
	zi	 = cmplx(0.0, 1.0)
	dx	 = 0.2
	dt	 = 0.0025/(dx*dx)
	                                       ! initial momentum, position
  k0x	 = 0.0; 	k0y	 = 2.5			
	x0	 = 0.0;   y0	 = - 7.0
	max	 = 90
	                                                 ! clear the arrays
  Do i = 1, 91                                            
	   Do j = 1, 91
		   Do k = 1, 2
			   psi(i, j, k) = 0.0
			   psr(i, j, k) = 0.0
		   End Do
	   End Do
   End Do
                                              ! initial wave function
		y		 = - 9.0
		Do	j = 1, max + 1
		  x = - 9.0d0
			Do	i = 1, max + 1
			  exc				 = exp(zi*(k0x*x + k0y*y))
				a1 = exp( - 0.5*(((x - x0))**2 + ((y - y0))**2))
				psr(i, j, 1) = real(a1*exc)                      !  real part
				psi(i, j, 1) = aimag(a1*exc)                 !  imaginay part
				x					 = x + dx
		End Do
		y = y + dx
  End Do		
                       ! set potential slit width: 50 - 40 = 10 units
	Do	j = 1, max + 1						
	  Do	i = 1, max + 1
		  If ((j == 35).and.((i < 40).or.(i > 51)))then 
			  v(i, j) = 0.5
				else	
					v(i, j) = 0.0
				Endif					
		End Do 
	End Do
                                         ! propagate psi through time
  Do	n = 1, time	 
                           ! compute real wave packet and probability
	  Do	j = 2, max
		  Do	i = 2, max
			    a2 = v(i, j)*psi(i, j, 1) + 2.0d0*dt*psi(i, j, 1)
				a1 = psi(i+1,j,1) + psi(i-1,j,1) +psi(i,j+1,1) + psi(i,j-1,1)
				psr(i, j, 2) = psr(i, j, 1) - dt*a1 + 2.0*a2
				If (n == time) then
				  p2(i,j) = psr(i,j,1)*psr(i,j,1) + psi(i,j,1)*psi(i, j, 1)
				Endif					
			End Do	
      psr(1, j, 2)		 = psr(2, j, 2)! at x edges derivative =0
			psr(max + 1, j, 2) = psr(max, j, 2)									 
		End Do	 
                                              ! imaginary part of psi
		Do	j = 2, max
		  Do	i = 2, max
			    a2 = v(i, j)*psr(i, j, 2) + 2.0*dt*psr(i, j, 2)
				a1 = psr(i+1,j,2) + psr(i-1,j,2) +psr(i,j-1,2) + psr(i,j+1,2)
				psi(i, j, 2) = psi(i, j, 1) + dt*a1 - 2.0*a2	 
			End Do
      psi(1, j, 2)		 = psi(2, j, 2)! at x edges derivative =0 
			psi(max + 1, j, 2) = psi(max, j, 2)									 
	  End Do					
		                                                     ! new -> old
    Do	j = 1, max + 1	                                       
		  Do	i = 1, max + 1
			    psi(i, j, 1) = psi(i, j, 2)
				psr(i, j, 1) = psr(i, j, 2)
		  End Do	 
		End Do									
  End Do		 
           ! write probabilities & potential scaled by 0.025 (to fit)
  Do	j = 2, max, 3
	  Do	i = 2, max, 2
		  write(9, 11)p2(i, j) + v(i, j)
		End Do	
		write(9, *) ' '			
  End Do
 11 format (E12.6)			 
	close(9)
	Stop 'data saved in slit.dat'
End