Relativistic Potentials with Rational Extensions

TL;DR

This paper develops new relativistic quantum potentials that are isospectral to known systems but lack shape invariance, expanding the class of solvable models in relativistic quantum mechanics.

Contribution

It introduces a method to construct isospectral Hamiltonians for relativistic potentials without relying on shape invariance, a common assumption in solvable models.

Findings

Constructed isospectral Hamiltonians for Dirac Oscillator and Hydrogen-like atom.

Extended the class of exactly solvable relativistic quantum models.

Provided new insights into the spectral properties of relativistic potentials.

Abstract

In this paper, we construct isospectral Hamiltonians without shape invariant potentials for the relativistic quantum mechanical potentials such as the Dirac Oscillator and Hydrogen-like atom.