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Interbasis "Sphere-Cylinder" Expansions for the Oscillator in the Three-Dimensional Space of Constant Positive Curvature

George S. Pogosyan
S. I. Vinitsky
Year: 1994
Keywords: interbasis, sphere-cylinder, expansions, oscillator, three-dimension, space, constant positive curvature, energy

In recent years, systems with accidental degeneracy in spaces of constant curvature have been in the focus of attention of many researches due to their nontrivial symmetry.

These systems have first been considered by Schrodinger who used the factorization method to solve the Schodinger equation and to find the energy spectrum for the harmonic potential being an analog of the Coulomb potential on the 3-sphere and showed that like in the case of flat space there occurs complete degeneracy of energy levels in orbital and azimuthal quantum numbers. Later, Infeld and Schild have treated this problem for the three-dimensional space of constant negative curvature.