Generalized MICZ-Kepler systems on three-dimensional sphere and hyperboloid

TL;DR

This paper introduces generalized MICZ-Kepler systems on curved spaces like the sphere and hyperboloid, deriving their energy spectra and wave functions, and demonstrating their minimal superintegrability.

Contribution

It constructs new analogs of the MICZ-Kepler system on curved geometries and analyzes their spectral and integrability properties.

Findings

Systems are minimally superintegrable.

Energy spectra and wave functions are explicitly constructed.

Analog systems extend Kepler problem to curved spaces.

Abstract

We propose analogs of the generalized MICZ-Kepler system on the three-dimensional sphere and (two-sheet) hyperboloid. We then construct their energy spectra and normalized wave functions, concluding that the suggested systems are minimally superintegrable.