Rationally extended shape invariant potentials in arbitrary D-dimensions associated with exceptional $X_m$ polynomials

TL;DR

This paper constructs rationally extended shape invariant potentials in arbitrary D-dimensions using point canonical transformation, with solutions expressed via exceptional orthogonal polynomials, maintaining isospectrality and shape invariance.

Contribution

It introduces a method to generate extended potentials in any dimension with solutions in terms of X_m exceptional polynomials, expanding solvable quantum models.

Findings

Potentials are isospectral to traditional counterparts.

Solutions involve X_m Laguerre or Jacobi polynomials.

Potentials exhibit translational shape invariance.

Abstract

Rationally extended shape invariant potentials in arbitrary D-dimensions are obtained by using point canonical transformation (PCT) method. The bound-state solutions of these exactly solvable potentials can be written in terms of X_m Laguerre or X_m Jacobi exceptional orthogonal polynomials. These potentials are isospectral to their usual counterparts and possess translationally shape invariance property.