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/quantum/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 May 5, 2016, 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 5 May 2016).

Belloni, Mario, and Wolfgang Christian. Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach. Vers. 1.0. 2008. 5 Feb. 2008. 5 May 2016 <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 = {2016},
Number = {5 May 2016},
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 2016 %N 5 May 2016 %7 1.0 %8 February 5, 2008 %9 application/java %U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=6475&DocID=273

Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.

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.