New exact solutions for polynomial oscillators in large dimensions

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dc.creatorZnojil, Miloslav
dc.creatorYanovich, Denis
dc.creatorGerdt, Vladimir P.
dc.date2003-02-19
dc.date2003-04-22
dc.date.accessioned2026-07-07T04:29:49Z
dc.date.available2026-07-07T04:29:49Z
dc.descriptionA new type of exact solvability is reported. We study the general central polynomial potentials (with 2q anharmonic terms) which satisfy the Magyari's partial exact solvability conditions (this means that they possess a harmonic-oscillator-like wave function proportional to a polynomial of any integer degree N). Working in the space of a very large dimension D for simplicity, we reveal that in contrast to the usual version of the model in finite dimensions (requiring a purely numerical treatment of the Magyari's constraints), our large D problem acquires an explicit, closed form solution at all N and up to q = 5 at least. This means that our effective secular polynomials (generated via the standard technique of Groebner bases) happen to be all fully factorizable in an utterly mysterious manner (mostly, over integers).
dc.descriptionslightly revised (new abstract, two equations added for clarity): 24 pages incl. 4 tables
dc.identifierhttps://arxiv.org/abs/math-ph/0302046
dc.identifierhttp://arxiv.org/abs/math-ph/0302046
dc.identifierJ. Phys. A: Math. Gen. 36 (2003) 6531-6549.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57296
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subject81Q05
dc.titleNew exact solutions for polynomial oscillators in large dimensions
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