Anisotropic Higgs oscillator

TL;DR

This paper generalizes the anisotropic Higgs oscillator to higher dimensions and explores related Kepler-like systems with additional potentials, detailing their symmetries and mathematical structure.

Contribution

It introduces a higher-dimensional version of the anisotropic Higgs oscillator and related systems, expanding their theoretical framework and symmetry analysis.

Findings

Derived potentials and symmetry generators in ambient Euclidean space.

Extended the anisotropic oscillator to higher dimensions.

Analyzed related Kepler-like systems with additional potentials.

Abstract

We present the higher-dimensional generalization of anisotropic (pseudo)spherical oscillator suggested recently in [arXiv:0710.5001], and the related spherical and pseudosperical generalizations (MICZ-)Kepler like systems with Stark term and $\cos\theta$ potential. We write down the potentials and hidden symmetry generators of these systems, in terms of ambient Euclidean space.