!--------------------------------------------------------------- !Program name: HYDROGEN-RADIAL !Radial equation of the hydrogen-like atom !Objective: plot the radial wave function for each n,l pair ! The equation is atomic units !--------------------------------------------------------------- !The Coulomb potential energy equation is: ! V(r) = -2Z/r ! The ceentrifugal potential equation is: ! VL=l(l+1)/r^2 ! The energy is: ! E=-2*Z/n^2 !--------------------------------------------------------------- ! Use of Numerov method to find the wave function ! Function fn from Numerov equation is ! Fn = 1 + K2*h^2/12 , where K2=-2(Veff - E) ! In the code, h is changed into dr !--------------------------------------------------------------- Program hydrogen Implicit none integer :: mesh, n, l, i, j, zeta, m, maxiter=100 Real*8 rmin, dr, zmesh, y_out_m double precision :: e, fh12, norm, eps=1.0E-6 double precision, allocatable :: r(:), r2
!--------------------------------------------------------------- !Program name: HYDROGEN-POTENTIAL !Objective: plot the effective potential energy as a function of radial distance !--------------------------------------------------------------- !The Coulomb potential energy equation is: ! V(r) = -KZq 2 /r = -(Kq 2 )(Z/r) ! K(Coulomb constant)= 9*10 9 Nm 2 C -2 ! q = - 1.602 x 10 -19 C ! Kq 2 =2.3 x 10 -28 ! The unit is Joule. We have to change into Rydberg. !---------------------------------------------------- ! The V(centrifugal) equation is: ! Vcent=6.1 x 10 -39 l(l+1)/r 2 (see text) ! The unit is Joule. We have to change into Rydberg !--------------------------------------------------------------- ! The unit of the radial distance, r, is meter. !--------------------------------------------------------------- Program hydrogen Implicit none integer :: mesh, n, l, i, zeta Real*8 rmin, dr, rmax double precision :: oldr, e, kq2, h2m
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