Infinite families of shape invariant potentials with n parameters subject to translation

TL;DR

This paper introduces new families of shape invariant potentials with multiple parameters, enabling novel spectral dependencies and potential applications in physical quantity engineering.

Contribution

It presents the construction of infinite families of shape invariant potentials with n parameters, expanding the theoretical framework and practical possibilities.

Findings

New spectral dependencies discovered

Explicit examples of shape invariant potentials provided

Potential for engineering physical quantities demonstrated

Abstract

We find new families of shape invariant potentials depending on n>=1 parameters subject to translation by the inclusion of non-trivial invariants. New dependencies of the spectra are found, and it opens the door to the engineering of physical quantities in a novel way. A number of examples are explicitly constructed.