! 	  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				 
! 		
! 	 qmc.f90: Feynman path integral for	ground state wave Function																					 
 
Program qmc

  Implicit none
	Integer :: i, j, max, element, prop(100)
	Real*8 :: change, ranDom, energy, newE, oldE, out, path(100)
	
	max	 = 250000
	open(9, FILE = 'qmc.dat', Status = 'Unknown')
	                                     ! initial path and probability
	Do	j = 1, 100
		path(j) = 0.0
		prop(j) = 0 
	End Do
	                                      ! find energy of initial path
  oldE = energy(path, 100)                    
	                            ! pick random element, change by random
  Do	i = 1, max
    element = ranDom()*100 + 1                        
  	change	 = ((ranDom() - 0.5)*2)                 
		path(element) = path(element) + change
    newE = energy(path, 100)                   ! find new energy
		                                           ! Metropolis algorithm
    
		If ((newE > oldE) .AND. (exp( - newE + oldE) < ranDom())) then
		  path(element) = path(element) - change
		EndIf
		                                           ! add up probabilities
    Do	j = 1, 100
		  element = path(j)*10 + 50						 
			prop(element) = prop(element) + 1              
		End Do
		oldE = newE
  End Do
	                                        ! write output data to file
  Do	j = 1, 100
		out = prop(j)
		write(9, *) j - 50, out/max                 
	End Do
	close(9)
	Stop 'data saved in qmc.dat'
End Program qmc
                           ! Function calculates energy of the system
Function energy(array, max)
	Implicit none
	Integer :: i, max
	Real*8 :: energy, array(max)
	energy = 0
	Do	i = 1, (max - 1)
	  energy = energy + (array(i+ 1) - array(i))**2 + array(i)**2
		End Do
	Return
End