Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach

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written by Mario Belloni and Wolfgang Christian

The Time Development in Quantum Mechanics paper describes the suite of open source programs that numerically calculate and visualize the evolution of arbitrary initial quantum-mechanical bound states. The calculations are based on the expansion of an arbitrary wave function in terms of basis vectors in a reduced Hilbert space. The approach is stable, fast, and accurate at depicting the long-time dependence of complicated bound states. Several real-time visualizations, such as the position and momentum expectation values and the Wigner quasiprobability distribution for the position and momentum, can be shown. We use these computational tools to study the time-dependent properties of quantum-mechanical systems and discuss the effectiveness of the algorithm.

American Journal of Physics: Volume 76, Issue 4&5, Pages 385-392

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Published: April 1, 2008

Subjects	Levels	Resource Types
Education Practices - Curriculum Development - Technology = Computers General Physics - Computational Physics Quantum Physics - Approximation Techniques - Bound State Systems	- Upper Undergraduate - Graduate/Professional	- Instructional Material = Interactive Simulation - Reference Material

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Access Rights:: Limited free access
Restriction:: © 2008 Mario Belloni and Wolfgang Christian
DOI:: 10.1119/1.2837810
Keywords:: OSP, Open Source Physics, numerical, quantum mechanics, reduced Hilbert space, time development
Record Creator:: Metadata instance created May 29, 2008 by Mario Belloni
Record Updated:: April 17, 2009 by Anne Cox
Last Update when Cataloged:: April 1, 2008
Other Collections:: The Open Source Physics

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Record Link

<a href="https://www.compadre.org/portal/items/detail.cfm?ID=7288">Belloni, Mario, and Wolfgang Christian. "Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach." Am. J. Phys. 76, no. 4&5, (April 1, 2008): 385-392.</a>

AIP Format

M. Belloni and W. Christian, , Am. J. Phys. 76 (4&5), 385 (2008), WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7288&DocID=458).

AJP/PRST-PER

M. Belloni and W. Christian, Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach, Am. J. Phys. 76 (4&5), 385 (2008), <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7288&DocID=458>.

APA Format

Belloni, M., & Christian, W. (2008, April 1). Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach. Am. J. Phys., 76(4&5), 385-392. Retrieved May 22, 2025, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7288&DocID=458

Chicago Format

Belloni, Mario, and Wolfgang Christian. "Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach." Am. J. Phys. 76, no. 4&5, (April 1, 2008): 385-392, https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7288&DocID=458 (accessed 22 May 2025).

MLA Format

Belloni, Mario, and Wolfgang Christian. "Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach." Am. J. Phys. 76.4&5 (2008): 385-392. 22 May 2025 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7288&DocID=458>.

BibTeX Export Format

@article{ Author = "Mario Belloni and Wolfgang Christian", Title = {Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach}, Journal = {Am. J. Phys.}, Volume = {76}, Number = {4&5}, Pages = {385-392}, Month = {April}, Year = {2008} }

Refer Export Format

%A Mario Belloni %A Wolfgang Christian %T Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach %J Am. J. Phys. %V 76 %N 4&5 %D April 1, 2008 %P 385-392 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7288&DocID=458 %O application/pdf

EndNote Export Format

%0 Journal Article %A Belloni, Mario %A Christian, Wolfgang %D April 1, 2008 %T Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach %J Am. J. Phys. %V 76 %N 4&5 %P 385-392 %8 April 1, 2008 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=7288&DocID=458

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

Covers the Same Topic As Numerical Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach

The American Journal of Physics article on Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach is the basis for this Launcher package. The package is an interactive version of the materials found in the AJP paper as well as additional curricular material.

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