2003/09/18 by Miloslav Znojil, Denis Yanovich
Physics and Astronomy · Mathematics · #math-ph #math.MP #math.NT #msc:15A36 #msc:11C08 #msc:12D05 #msc:34E05 #msc:81Q05
published as Proc. Inst. Math. NAS Ukr. 50, part II (2004), 1010 - 1017. · Talk for The Fifth International Conference "Symmetry in Nonlinear Mathematical Physics" held June 23-29, 2003, at the Institute of Mathematics in Kyiv (Kiev), Ukraine
arxiv created 2003/09/18 · arxiv updated 2009/12/01
Schroedinger 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.