Group theoretic approach to rationally extended shape invariant potentials

TL;DR

This paper uses a group theoretic approach to derive the bound state spectra of extended shape invariant potentials, including complex PT-symmetric cases, by modifying potential algebra generators.

Contribution

It introduces a new operator to express extended potentials in terms of Casimir operators, linking potential algebra with shape invariance.

Findings

Exact spectra for extended potentials obtained

Connection established between potential algebra and shape invariance

Applicable to both real and PT-symmetric complex potentials

Abstract

The exact bound state spectrum of rationally extended shape invariant real as well as $PT$ symmetric complex potentials are obtained by using potential group approach. The generators of the potential groups are modified by introducing a new operator $U (x, J_3 \pm 1/2 )$ to express the Hamiltonian corresponding to these extended potentials in terms of Casimir operators. Connection between the potential algebra and the shape invariance is elucidated.