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Mostrando postagens de Junho, 2021

HYDROGEN-RADIAL

!--------------------------------------------------------------- !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

HYDROGEN-POTENTIAL

  !--------------------------------------------------------------- !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

ONE_PART_QHO

  !--------------------------------------------------------------- !Program name: ONE_PART_QHO !Original code: Giannozzi,P., Ercolessi, F. and Gironcoli, S. !Modified by Caio Lima Firme !One particle quantum harmonic oscillator !PARABOLIC POTENTIAL WELL !Objective: to plot the wave function for each node !--------------------------------------------------------------- !The dimensionless physical quantities: !Potential energy: V(x)=0.5X^2    ! Energy: E=1/2+n !--------------------------------------------------------------- ! Use of Numerov method to find the wave function ! Function fn from Numerov equation is ! Fn = 1 + K2*h^2/12 , where K2=2m/((H/2pi)^2)*(E-V) ! H=Planck constant !-------------------------------------------------------------- -   integer :: grid, i, icl   integer :: n, hn, ncross, j, iter   double precision :: xmax, h, fh12, norm, djump, fac   double precision :: Vupper, Vlower, e, k   double precision :: x(0:300), y(0:300), V