Lie theory and separation of variables. 6. The equation iUt + ∆2U = 0

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dc.contributor.authorBoyer, C.P.
dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorMiller, W., Jr.
dc.date.accessioned2008-11-03T03:30:21Z
dc.date.available2008-11-03T03:30:21Z
dc.date.issued1975-03
dc.description.abstractThis paper constitutes a detailed study of the nine−parameter symmetry group of the time−dependent free particle Schrödinger equation in two space dimensions. It is shown that this equation separates in exactly 26 coordinate systems and that each system corresponds to an orbit consisting of a commuting pair of first− and second−order symmetry operators. The study yields a unified treatment of the (attractive and repulsive) harmonic oscillator, linear potential and free particle Hamiltonians in a time−dependent formalism. Use of representation theory for the symmetry group permits simple derivations of addition and expansion theorems relating various solutions of the Schrödinger equation, many of which are new.en_US
dc.format.mimetypeapplication/pdf
dc.identifier.citationBoyer, C.P., Kalnins, E.G. & Miller, W., Jr. (1975). Lie theory and separation of variables. 6. The equation iUt + ∆2U = 0. Journal of Mathematical Physics, 16, 499.en_US
dc.identifier.doi10.1063/1.522573en_US
dc.identifier.issn0022-2488
dc.identifier.urihttps://hdl.handle.net/10289/1244
dc.language.isoen
dc.relation.urihttp://link.aip.org/link/?JMAPAQ/16/499/1en_US
dc.rightsCopyright 1975 American Institute of Physics. 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 the Journal of Mathematical Physics and may be found at http://jmp.aip.org/jmp/top.jspen_US
dc.subjectMathematicsen_US
dc.titleLie theory and separation of variables. 6. The equation iUt + ∆2U = 0en_US
dc.typeJournal Articleen_US
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