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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorMiller, W., Jr.
dc.date.accessioned2008-11-03T19:52:30Z
dc.date.available2008-11-03T19:52:30Z
dc.date.issued1974-10
dc.identifier.citationKalnins, E.G. & Miller, W., Jr. (1974). Lie theory and separation of variables. 5. The equations iUt + Uxx = 0 and iUt + Uxx −c/x2 U = 0. Journal of Mathematical Physics, 15, 1728.en_US
dc.identifier.issn0022-2488
dc.identifier.urihttps://hdl.handle.net/10289/1248
dc.description.abstractA detailed study of the group of symmetries of the time-dependent free particle Schrödinger equation in one space dimension is presented. An orbit analysis of all first order symmetries is seen to correspond in a well-defined manner to the separation of variables of this equation. The study gives a unified treatment of the harmonic oscillator (both attractive and repulsive), Stark effect, and free particle Hamiltonians in the time dependent formalism. The case of a potential c/x2 is also discussed in the time dependent formalism. Use of representation theory for the symmetry groups permits simple derivation of expansions relating various solutions of the Schrödinger equation, several of which are new.en_US
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.relation.urihttp://link.aip.org/link/?JMAPAQ/15/1728/1en_US
dc.rightsCopyright 1974 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. 5. The equations iUt + Uxx = 0 and iUt + Uxx −c/x2 U = 0en_US
dc.typeJournal Articleen_US
dc.identifier.doi10.1063/1.1666533en_US


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