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Total time derivatives of operators in elementary quantum mechanics

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Andrews, Mark

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The use of a total time derivative of operators, that depends on the time evolution of the wave function as well as on any intrinsic time dependence in the operators, simplifies the formal development of quantum mechanics and allows its development to more closely follow the corresponding development of classical mechanics. We illustrate the use of the total time derivative for a free particle, the linear potential, the harmonic oscillator, and the repulsive inverse square potential. In these...[Show more]

dc.contributor.authorAndrews, Mark
dc.date.accessioned2015-10-09T04:38:09Z
dc.date.available2015-10-09T04:38:09Z
dc.identifier.issn0002-9505
dc.identifier.urihttp://hdl.handle.net/1885/15855
dc.description.abstractThe use of a total time derivative of operators, that depends on the time evolution of the wave function as well as on any intrinsic time dependence in the operators, simplifies the formal development of quantum mechanics and allows its development to more closely follow the corresponding development of classical mechanics. We illustrate the use of the total time derivative for a free particle, the linear potential, the harmonic oscillator, and the repulsive inverse square potential. In these cases, operators whose total time derivative is zero can be found and yield general properties of wave packets and several useful time-dependent solutions of Schrödinger’s equation, including the propagator.
dc.publisherAmerican Association of Physics Teachers
dc.rights© 2003 American Association of Physics Teachers. Publisher permission to archive the version was granted via email on 19/11/2015. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in American Journal of Physics and may be found at https://doi.org/10.1119/1.1531579
dc.sourceAmerican Journal of Physics
dc.titleTotal time derivatives of operators in elementary quantum mechanics
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume71
dc.date.issued2003
local.identifier.absfor010501
local.identifier.ariespublicationMigratedxPub16349
local.publisher.urlhttp://www.aapt.org/
local.type.statusPublished Version
local.contributor.affiliationAndrews, Mark, College of Physical and Mathematical Sciences, CPMS Research School of Physics and Engineering, Department of Quantum Science, The Australian National University
local.bibliographicCitation.issue4
local.bibliographicCitation.startpage326
local.bibliographicCitation.lastpage332
local.identifier.doi10.1119/1.1531579
dc.date.updated2015-12-12T08:20:52Z
local.identifier.scopusID2-s2.0-0037392722
CollectionsANU Research Publications

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