Geometric models of (d+1)-dimensional relativistic rotating oscillators

TL;DR

This paper introduces geometric models for quantum relativistic rotating oscillators in various dimensions, solvable analytically with energy levels and eigenfunctions, all sharing the same nonrelativistic harmonic oscillator limit.

Contribution

It presents a new class of analytically solvable geometric models for relativistic oscillators in arbitrary dimensions based on deformed anti-de Sitter backgrounds.

Findings

Models are analytically solvable with explicit energy levels.

Eigenfunctions are explicitly derived and normalized.

All models share the same nonrelativistic harmonic oscillator limit.

Abstract

Geometric models of quantum relativistic rotating oscillators in arbitrary dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It is shown that these models are analytically solvable, deriving the formulas of the energy levels and corresponding normalized energy eigenfunctions. An important property is that all these models have the same nonrelativistic limit, namely the usual harmonic oscillator.