Motion on the n-dimensional ellipsoid under the influence of a harmonic force revisited

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dc.creatorDita, Petre
dc.date2002-11-28
dc.date.accessioned2026-07-07T10:49:31Z
dc.date.available2026-07-07T10:49:31Z
dc.descriptionThe $n$ integrals in involution for the motion on the $n$-dimensional ellipsoid under the influence of a harmonic force are explicitly found. The classical separation of variables is given by the inverse momentum map. In the quantum case the Schrödinger equation separates into one-dimensional equations that coincide with those obtained from the classical separation of variables. We show that there is a more general orthogonal parametrisation of Jacobi type that depends on two arbitrary real parameters. Also if there is a certain relation between the spring constants and the ellipsoid semiaxes the motion under the influence of such a harmonic potential is equivalent to the free motion on the ellipsoid.
dc.descriptionLatex2e, 18 pages
dc.identifierhttps://arxiv.org/abs/hep-th/0211273
dc.identifierhttp://arxiv.org/abs/hep-th/0211273
dc.identifierJ.Phys.A36:10159-10172,2003
dc.identifierdoi:10.1088/0305-4470/36/40/003
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184243
dc.subjectHigh Energy Physics - Theory
dc.subjectHigh Energy Physics - Phenomenology
dc.subjectMathematical Physics
dc.subjectExactly Solvable and Integrable Systems
dc.titleMotion on the n-dimensional ellipsoid under the influence of a harmonic force revisited
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