Spectral manipulation of the trigonometric Rosen-Morse potential through supersymmetry

TL;DR

This paper demonstrates how first and second-order supersymmetry transformations can be used to modify specific energy levels of the trigonometric Rosen-Morse potential, creating new exactly solvable quantum Hamiltonians.

Contribution

It constructs supersymmetric partners of the Rosen-Morse potential and illustrates spectral manipulation without introducing singularities, advancing exactly solvable models.

Findings

Successfully generated new solvable potentials with altered spectra

Identified solutions suitable for non-singular supersymmetric transformations

Provided explicit examples of spectral manipulation

Abstract

The first and second-order supersymmetry transformations can be used to manipulate one or two energy levels of the initial spectrum when generating new exactly solvable Hamiltonians from a given initial potential. In this paper, we will construct the first and second-order supersymmetric partners of the trigonometric Rosen-Morse potential. Firstly, it is identified a set of solutions of the initial stationary Schr\"odinger equation which are appropriate for implementing in a simple way non-singular transformations, without inducing new singularities in the built potential. Then, the way the spectral manipulation works is illustrated through several specific examples.