! 	  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				 
! 						
! 	 sqwell.f90: Solves the t-dependent Schroedinger equation for a
!     Gaussian wavepacket in a infinite square well potential			

Program sqwell

  Implicit None
	Real*8 :: psr(751, 2), psi(751, 2), p2(751)
	Real*8 :: dx, k0, dt, x, pi
	Integer :: i, j, n, max
	Complex exc, zi
	
	Common /values/dx, dt
	
	open(9, FILE = 'sqwell.dat', Status = 'Unknown')
	max		 = 750
	pi	 = 3.14159265358979323846
	zi	 = CMPLX(0.0, 1.0)
	dx	 = 0.02
	k0	 = 17.0*pi
	dt	 = dx*dx	
	                                                 ! clear the arrays
  Do i = 1, 751                                          
	  Do j = 1, 2
		  psr(i, j) = 0.0
		  psi(i, j) = 0.0
		  p2(i) = 0.0
	  End Do
  End Do
	                                               ! initial conditions
    x		 = 0.0                                         
		Do	i = 1, max + 1
		  exc			 = exp(zi*k0*x)
      psr(i, 1) = real(exc*exp( - 0.5*(2.0*(x - 5.0))**2))! real part
			psi(i, 1) = aimag(exc*exp( - 0.5*(2.0*(x - 5.0))**2))    ! imag
			x				 = x + dx
		End Do
                                    ! propagate solution through time
    Do	n = 1, 6000
      Do	i = 2, max! real part & prob				
			  psr(i, 2) = psr(i, 1) - dt*(psi(i+ 1, 1) + psi(i- 1, 1)&
									 - 2.0*psi(i, 1))/(2.0*dx*dx)
				p2(i)		 = psr(i, 1)*psr(i, 2) + psi(i, 1)*psi(i, 1)		 
			End Do
			Do	i = 2, max                                 ! imaginary part
        psi(i, 2) = psi(i, 1) + dt*(psr(i+ 1, 2) + psr(i- 1, 2)&
										 - 2.0*psr(i, 2))/(2.0*dx*dx)	 
			End Do  
			                                           ! selective printout
      If (Mod(n, 300) == 0) then                       
			  Do	i = 1, max + 1, 15
				  write(9, 11) p2(i)
				End Do
				write(9, *) ' '	 
			Endif
			                                             ! new soltn -> old
      Do	i = 1, max + 1                                 
			  psi(i, 1) = psi(i, 2)
				psr(i, 1) = psr(i, 2)
			End Do										 
		End Do
 11 format (E12.6)
	close(9)		 
  Stop 'data saved in sqwell.dat'
End