The Eigenstate Superposition model illustrates the fundamental building blocks of one-dimensional quantum mechanics, the energy eigenfunctions ψ_{n}(x) and energy eigenvalues E_{n}. The user enters the expansion coefficients into a table and the simulation uses the superposition principle to construct and display a time-dependent wave function using either infinite square well (ISW) or simple harmonic oscillator (SHO) eigenfunctions.

The Eigenstate Superposition model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_qm_Superposition.jar file will run the program if Java is installed.

Please note that this resource requires
at least version 1.5 of
Java (JRE).

Eigenstate Superposition source code
The source code zip archive contains an XML representation of the eigenstate superposition model. Unzip this archive in your EJS workspace to compile and run… more... download 29kb .zip
Published: September 11, 2008

Author: MuckrakerW M
Posted: October 20, 2014 at 9:38PM
Source: The Quantum Exchange collection

The ejs simulator certainly helps you to get a better understanding of how to compute the eigenfunctions and their corresponding eigenvalues. But this is done when you normalize the wave function, which, in order to be normalized must be square integrable and finite. Then you can observe depending on quantum number n the various energy eigenfunctions and values in the 1-d infinite square well as they oscillate at different wavelengths and amplitudes you can set again depending on your bounds, i.e. -a < x < a. Moreover that you do all this because the eigenfunctions are standing waves in a bound state and not traveling waves.

On the other hand, the harmonic oscillator is a bit different. That is, one must realize using such wave functions to solve the Schrodinger equation would not be so easy to do because of several problems that develop. One such being the quadratic x^2 and switching the constant -hbar/2m away from y'' in order to make it have a coefficient of one since it is the highest order derivative in the differential equation.

To make life a whole lot simpler we have to use the Hermite polynomials for the SHO which are not hard at all. For the most part if you know how to do power series in calculus then it is relatively easy to find solutions to the S.E. using Hermite polynomials and their recurrent relation from the Hermite differential equation. http://www.globalbabbler.com

Thank you for your comment. This is true, the Superposition Model uses the simple harmonic oscillator wavefunctions using the Hermite Polynomials, as outlined in the description.

W. Christian, Computer Program EIGENSTATE SUPERPOSITION MODEL (2008), WWW Document, (http://www.compadre.org/Repository/document/ServeFile.cfm?ID=7945&DocID=684).

Christian, W. (2008). Eigenstate Superposition Model [Computer software]. Retrieved October 21, 2014, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=7945&DocID=684

%A Wolfgang Christian %T Eigenstate Superposition Model %D August 31, 2008 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=7945&DocID=684 %O application/java

%0 Computer Program %A Christian, Wolfgang %D August 31, 2008 %T Eigenstate Superposition Model %8 August 31, 2008 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=7945&DocID=684

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