#
Introduction to Computational Physics - Class Project

# Solution of the Schroedinger Equation in a Realistic
Quantum Well

## Aleksandra Milovanovich
- Physics, Technion.

This program solves the time independent and time dependent Schroedinger
eqation for particle in one dimenisional box. Two forms of potential are
available: a square well with a bump and "double parabola"
(polynomial in form a*x**4+b*x**2+c). You can choose the
center of the potential, it's half-width and height; the initial center
of the Gaussian
wavepacket and it's width; and the x-value that divides left from right (used
to evaluate probabilities).

First, the time independent Schroedinger eqation is solved
for the specific potential. You will be asked to give initial values for
the energy and energy step in the search for the energy eigenvalue.
When the eigenvalue
is found, the program solves the time dependent
Schroedinger equation for the
Gaussian wave packet with initial energy equal to eigenvalue of the energy.

Then, the
time independent Schroedinger equation is solved
using subroutine NUMERV (written by S.E. Koonin/D.C. Meredith,"Computational
Physics ") and time dependent Schroedinger equation by subroutine
TRIAG (ibid.).

Output - at each time step the text output displays unscaled
time, energy eigenvalue and left and right probabilities. Graphics output
can be obtained by using MATLAB program *wplot1.m - *it
plots |wavefunction|^2, potential and eigenvalue of energy on the same
graph.
This project uses FORTRAN and MATLAB; the programs can
be obtained with
http from the Computational Physics http server. They are
compiled with the command

" f77 qw.f -o qw.ex "

You then run the program and afterwards open
a window to matlab
and write wplot1 to start the matlab graphics. More information on
this project by *email.
*

###
Online material is available for the Fall 1997

*Computational
Physics Class*

Last updated on : Sun May 31
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