Supersymmetric partners for the associated Lame potentials

TL;DR

This paper derives the general solutions for the stationary Schrödinger equation with associated Lame potentials and constructs their supersymmetric partners using seed solutions within the spectral gaps.

Contribution

It provides a comprehensive method to generate supersymmetric partner potentials for associated Lame potentials at arbitrary energies.

Findings

Explicit general solutions for associated Lame potentials obtained.

Supersymmetric partners constructed using seed solutions in spectral gaps.

Method applicable to a wide range of energies within the potential's spectrum.

Abstract

The general solution of the stationary Schrodinger equation for the associated Lame potentials with an arbitrary real energy is found. The supersymmetric partners are generated by employing seeds solutions for factorization energies inside the gaps.