The radial supersymmetry of the (d+1)-dimensional relativistic rotating oscillators

TL;DR

This paper explores the supersymmetry properties of radial equations in relativistic rotating oscillator models across various dimensions, revealing shape invariance and simplified formulas for wave functions.

Contribution

It demonstrates the shape invariance of supersymmetric partner potentials in relativistic oscillators with deformed anti-de Sitter backgrounds, providing explicit Rodrigues formulas.

Findings

Shape invariance of radial potentials established

Simplified Rodrigues formulas for wave functions derived

Supersymmetry structure identified in relativistic models

Abstract

We study the supersymmetry of the radial problems of the models of quantum relativistic rotating oscillators in arbitrary dimensions, defined as Klein-Gordon fields in backgrounds with deformed anti-de Sitter metrics. It is pointed out that the shape invariance of the supersymmetric partner radial potentials leads to simple operators forms of the Rodrigues formulas for the normalized radial wave functions.