Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach

written by
Mario Belloni and
Wolfgang Christian

This self-contained file contains Open Source Physics programs for the teaching of time evolution and visualization of quantum-mechanical bound states. The suite of programs is based on the ability to expand an arbitrary wave function in terms of basis vectors in a reduced Hilbert space (the superposition principle). One can choose from several real-time visualizations, such as the position and momentum expectation values and the Wigner quasi-probability distribution for position and momentum. We describe how these tools can be used to study the long-term time-dependent properties of quantum-mechanical systems.

The materials and text of this resource appeared in an article of the same name in the Theme Double-Issue on Computation and Computer-based Instruction in the American Journal of Physics [Am. J. Phys. 76, No. 4&5, pp. 385-392 (2008)].

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

<a href="http://www.compadre.org/OSP/items/detail.cfm?ID=6475">Belloni, Mario, and Wolfgang Christian. Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach. February 5, 2008.</a>

M. Belloni and W. Christian, Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach, , Version 1.0 (2008), <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=6475&DocID=273>.

Belloni, M., & Christian, W. (2008, February 5). Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach. Retrieved August 4, 2015, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=6475&DocID=273

Belloni, Mario, and Wolfgang Christian. Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach. February 5, 2008. http://www.compadre.org/Repository/document/ServeFile.cfm?ID=6475&DocID=273 (accessed 4 August 2015).

Belloni, Mario, and Wolfgang Christian. Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach. Vers. 1.0. 2008. 5 Feb. 2008. 4 Aug. 2015 <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=6475&DocID=273>.

@misc{
Author = "Mario Belloni and Wolfgang Christian",
Title = {Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach},
Volume = {2015},
Number = {4 August 2015},
Month = {February 5, 2008},
Year = {2008}
}

%A Mario Belloni %A Wolfgang Christian %T Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach %D February 5, 2008 %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=6475&DocID=273 %O 1.0 %O application/java

%0 Electronic Source %A Belloni, Mario %A Christian, Wolfgang %D February 5, 2008 %T Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach %V 2015 %N 4 August 2015 %7 1.0 %8 February 5, 2008 %9 application/java %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=6475&DocID=273

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The Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach Package contains a collection of OSP programs for the study quantum-mechanical concepts. This article describes the OSP-based programs and shows how OSP-based materials can be used to study quantum-mechanical concepts.

The Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach Package contains curricular materials for the teaching of quantum mechanics using the QM Superposition Program.

The Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach Package contains curricular materials for the teaching of quantum mechanics using the QM Wigner Program.

The Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach Package contains curricular materials for the teaching of quantum mechanics using the QM Projection Program.