Rational Extension of Anisotropic Harmonic Oscillator Potentials in Higher Dimensions

TL;DR

This paper develops a supersymmetric rational extension of the quantum anisotropic harmonic oscillator in multiple dimensions, providing exact solutions using exceptional orthogonal polynomials and demonstrating isospectrality with traditional models.

Contribution

It introduces the first-order supersymmetric rational extension of multidimensional QAHOs, expanding the class of exactly solvable models with exceptional orthogonal polynomials.

Findings

Extended potentials are isospectral to conventional QAHOs.

Exact solutions are expressed in terms of exceptional orthogonal polynomials.

Applicable to full-line, half-line, and mixed boundary conditions.

Abstract

This paper presents the first-order supersymmetric rational extension of the quantum anisotropic harmonic oscillator (QAHO) in multiple dimensions, including full-line, half-line, and their combinations. The exact solutions are in terms of the exceptional orthogonal polynomials. The rationally extended potentials are isospectral to the conventional QAHOs.