Solution of Klein Gordon equation
by Reinaldo Baretti Machin
reibaretti2004@yahoo.com
www.oocities.org/reibaretti2004
www.oocities.org/serienumerica



c      c Klein Gordon equation
      implicit real*8(a-h,o-z)
      dimension psi(0:10000)
      u(x)=-z/x
      g(e,x)= (e-u(x))
      c=137.11d0
c      c=1.d4
      iter=20
      z=30.d0
c      e1=-1.2d0*(z**2/2.d0)
c      e2=.85d0* (-z**2/2.d0)
      e1=-490.d0
      e2=-440.d0
      e=e1
      deltae=(e2-e1)/dfloat(iter)
c      xf=.25d0
      nx=8000

      do 50 it=1,iter
      xf=-2.9d0*z/e
      dx=xf/dfloat(nx)
      psi(0)=1.d0
      psi(1)=-dx+psi(0)
      do 10 i=2,nx
      x1=dx*dfloat(i-1)
      psi(i)=-dx**2*( (g(e,x1)/c)**2+2.d0*g(e,x1))*psi(i-1)+
     $2.d0*psi(i-1) -psi(i-2) -2.d0*(dx/x1)*(psi(i-1)-psi(i-2))
10    continue
c      do 30 ip=0,nx,2
c      x=dx*dfloat(ip)
      print 110 ,x1,e, psi(nx)
c30    continue
20    continue
      e=e+deltae
50    continue
110   format(2x,'x,e,psi=',1x, 3(3x,e11.4))
      stop
      end
      
        x,e,psi=     0.1775E+00   -0.4900E+03    0.2587E-01
  x,e,psi=     0.1784E+00   -0.4875E+03    0.2061E-01
  x,e,psi=     0.1794E+00   -0.4850E+03    0.1529E-01
  x,e,psi=     0.1803E+00   -0.4825E+03    0.9908E-02
x,e,psi=     0.1812E+00   -0.4800E+03    0.4460E-02
  x,e,psi=     0.1822E+00   -0.4775E+03   -0.1055E-02
  x,e,psi=     0.1831E+00   -0.4750E+03   -0.6637E-02
  x,e,psi=     0.1841E+00   -0.4725E+03   -0.1229E-01
  x,e,psi=     0.1851E+00   -0.4700E+03   -0.1801E-01
  x,e,psi=     0.1861E+00   -0.4675E+03   -0.2380E-01
  x,e,psi=     0.1871E+00   -0.4650E+03   -0.2966E-01
  x,e,psi=     0.1881E+00   -0.4625E+03   -0.3559E-01
  x,e,psi=     0.1891E+00   -0.4600E+03   -0.4160E-01
  x,e,psi=     0.1901E+00   -0.4575E+03   -0.4768E-01
  x,e,psi=     0.1912E+00   -0.4550E+03   -0.5384E-01
  x,e,psi=     0.1922E+00   -0.4525E+03   -0.6008E-01
  x,e,psi=     0.1933E+00   -0.4500E+03   -0.6639E-01
  x,e,psi=     0.1944E+00   -0.4475E+03   -0.7278E-01
  x,e,psi=     0.1955E+00   -0.4450E+03   -0.7926E-01
  x,e,psi=     0.1966E+00   -0.4425E+03   -0.8582E-01