Time Development in Quantum Mechanics Using a Reduced Hilbert Space Approach

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.

<a href="http://www.compadre.org/OSP/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>

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

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

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 July 31, 2015, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=7288&DocID=458

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, http://www.compadre.org/Repository/document/ServeFile.cfm?ID=7288&DocID=458 (accessed 31 July 2015).

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. 31 July 2015 <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=7288&DocID=458>.

@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}
}

%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 http://www.compadre.org/Repository/document/ServeFile.cfm?ID=7288&DocID=458 %O application/pdf

%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 http://www.compadre.org/Repository/document/ServeFile.cfm?ID=7288&DocID=458

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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.