New type of exact solvability and of a hidden nonlinear dynamical symmetry in anharmonic oscillators

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dc.creatorZnojil, Miloslav
dc.creatorYanovich, Denis
dc.date2003-09-18
dc.date.accessioned2026-07-07T04:30:34Z
dc.date.available2026-07-07T04:30:34Z
dc.descriptionSchroedinger bound-state problem in D dimensions is considered for a set of central polynomial potentials (containing 2q coupling constants). Its polynomial (harmonic-oscillator-like, quasi-exact, terminating) bound-state solutions of degree N are sought at a (q+1)-plet of exceptional couplings/energies, the values of which comply with (the same number of) termination conditions. We revealed certain hidden regularity in these coupled polynomial equations and in their roots. A particularly impressive simplification of the pattern occurred at the very large spatial dimensions D where all the "multi-spectra" of exceptional couplings/energies proved equidistant. In this way, one generalizes one of the key features of the elementary harmonic oscillators to (presumably, all) non-vanishing integers q.
dc.descriptionTalk for The Fifth International Conference "Symmetry in Nonlinear Mathematical Physics" held June 23-29, 2003, at the Institute of Mathematics in Kyiv (Kiev), Ukraine
dc.identifierhttps://arxiv.org/abs/math-ph/0309047
dc.identifierhttp://arxiv.org/abs/math-ph/0309047
dc.identifierProc. Inst. Math. NAS Ukr. 50, part II (2004), 1010 - 1017.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57507
dc.subjectMathematical Physics
dc.subjectNumber Theory
dc.subject15A36; 11C08; 12D05; 34E05; 81Q05
dc.titleNew type of exact solvability and of a hidden nonlinear dynamical symmetry in anharmonic oscillators
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