Givens method

Finite difference method to solve the the time independent Shrödinger equation for a system on a one dimensional potential energy surface.

Usage:

In the file potential.f90 write a function named v(x) that receives the position at which the potential energy is evaluated and returns it. Notice distance is meters and energy in J. Example:

function v(x)
!analitical function of the potential (Morse Potential)                     
!the units of the potential must be in J.

implicit none

!De: well depth
!a: control of the width of the potential 
!re: equilibrium distance
!x: positions of the oscillator

real(8) :: De, a, re, v,x

re=1.275d-10 !m
De=7.10647d-19 !J
a=1.81181d10

v=De*(1-exp(-a*(x-re)))**2
endfunction

Variables to define:

• intv(1): Minimum distance of the oscillator used in the integration (m).
• intv(2): Maximum distance of the oscillator used in the integration (m).
• npoints: Integration points.
• mass1: Mass of particle 1 (kg).
• mass2: Mass of particle 2 (kg).

Compile the code with Makefile. Execute the program as:

./givens.x

A file wf.dat is produced with the following information:

#  Position      Potential         Energy          Function (state 1)  Function (state 2) ... 
                           ...

Results

The first bound states calculated with this program are shown.