Associated Lame and various other new classes of elliptic potentials from sl(2,R) and related orthogonal polynomials

TL;DR

This paper introduces new classes of elliptic potentials derived from sl(2,R) representations, providing explicit eigenvalues, spectra, and orthogonal polynomials, and demonstrating their reduction to known solvable potentials.

Contribution

It presents novel elliptic potentials from sl(2,R) representations and constructs their eigenfunctions and spectra, expanding the set of exactly solvable models.

Findings

Derived new elliptic potentials from sl(2,R) representations.

Explicitly calculated eigenvalues and spectra for these potentials.

Showed these potentials reduce to known solvable potentials in certain limits.

Abstract

Using representations of sl(2,R) generators which yield associated Lame Hamiltonians we obtain new classes of elliptic potentials. We explicitly calculate eigenvalues and spectra for these potentials and construct the associated orthogonal polynomials. We show that in the proper limit these potentials reduce to well-known exactly solvable potentials.