Physics – Mathematical Physics
Scientific paper
2003-09-18
Proc. Inst. Math. NAS Ukr. 50, part II (2004), 1010 - 1017.
Physics
Mathematical Physics
Talk for The Fifth International Conference "Symmetry in Nonlinear Mathematical Physics" held June 23-29, 2003, at the Institu
Scientific paper
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.
Yanovich Denis
Znojil Miloslav
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