Four-dimensional double singular oscillator

Abstract

The Schrödinger equation for the four-dimensional double singular oscillator is separable in Eulerian, doble polar and spheroidal coordinates in ${\mathrm{IR}}^4$. It is shown that the coefficients for the expansion of double polar basis in terms of the Eulerian basis can be expressed through the Clebsch-Gordan coefficients of the group SU(2) analytically continued to real values of their arguments. The coefficients for the expansions of the spheroidal basis in terms of the Eulerian and double polar bases are proved to satisfy three-term recursion relations.

10 pages

References in corpus (3)

• The generalized MIC-Kepler system
• ``Charge-Dyon" System As The Reduced Oscillator
• 4D singular oscillator and generalized MIC-Kepler system

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• Generalized five-dimensional Kepler system, Yang-Coulomb monopole and Hurwitz transformation
• A new family of $N$ dimensional superintegrable double singular oscillators and quadratic algebra $Q(3)\oplus so(n)\oplus so(N-n)$
• Generalized Kaluza-Klein monopole, quadratic algebras and ladder operators
• Superintegrable systems from block separation of variables and unified derivation of their quadratic algebras
• Superintegrable systems, polynomial algebra structures and exact derivations of spectra