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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

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