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dc.contributor.authorKalnins, Ernie G.
dc.contributor.authorMiller, W., Jr.
dc.contributor.authorPogosyan, G.S.
dc.coverage.spatialConference held at Kyiv, Ukraineen_NZ
dc.date.accessioned2009-01-11T20:13:22Z
dc.date.available2009-01-11T20:13:22Z
dc.date.issued2004
dc.identifier.citationKalnins, E.G., Miller, W., Jr. & Pogosyan, G.S.(2004). Infinite order symmetries for two-dimensional separable Schrödinger equations. In Proceedings of Institute of Mathematics of NAS of Ukraine, 50(1), 184-195.en
dc.identifier.urihttps://hdl.handle.net/10289/1763
dc.description.abstractConsider a non-relativistic Hamiltonian operator H in 2 dimensions consisting of a kinetic energy term plus a potential. We show that if the associated Schrödinger eigenvalue equation admits an orthogonal separation of variables, there is a calculus to describe the (in general) infinite-order differential operator symmetries of the Schrödinger equation. The calculus is formal but can be made rigorous when all functions in the eigenvaue equation are analytic. The infinite-order calculus exhibits structure that is not apparent when one studies only finite-order symmetries. The search for finite-order symmetries can then be reposed as one of looking for solutions of a coupled system of PDEs that are polynomial in certain parameters. We go further and extend the calculus to the situation where the Schrödinger equation admits a second-order symmetry operator, not necessarily associated with orthogonal separable coordinates.en
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherInstitute of Mathematics of the National Academy of Sciences of Ukraineen_NZ
dc.relation.urihttp://www.imath.kiev.ua/~snmp2003/Proceedings/miller.pdfen
dc.rightsThis article has been published in Proceedings of Institute of Mathematics of NAS of Ukraine. ©2004 Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv(Kiev), Ukraine.en
dc.subjectmathematicsen
dc.subjectSchrödinger equationen
dc.titleInfinite order symmetries for two-dimensional separable Schrödinger equationsen
dc.typeConference Contributionen
dc.relation.isPartOfFifth International Conference Symmetry in Nonlinear Mathematical Physicsen_NZ
pubs.begin-page184en_NZ
pubs.elements-id15972
pubs.end-page195en_NZ
pubs.finish-date2003-06-29en_NZ
pubs.place-of-publicationUkraineen_NZ
pubs.start-date2003-06-23en_NZ
pubs.volumeProceedings of Institute of Mathematics of National Academy of Sciences of Ukraine: Mathematics and its Applications Vol 50en_NZ


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