Supersymmetric Method for Constructing Quasi-Exactly Solvable Potentials

TL;DR

This paper introduces a supersymmetric approach to systematically construct quasi-exactly solvable potentials with two known eigenstates, providing explicit energy levels and wave functions, and presenting new potential examples.

Contribution

It presents a novel supersymmetric method for generating QES potentials with explicitly known states, advancing the theoretical framework for solvable quantum models.

Findings

Derived general expressions for QES potentials with two known states

Constructed new examples of QES potentials using the method

Provided explicit energy levels and wave functions for these potentials

Abstract

We propose a new method for constructing the quasi-exactly solvable (QES) potentials with two known eigenstates using supersymmetric quantum mechanics. General expression for QES potentials with explicitly known energy levels and wave functions of ground state and excited state are obtained. Examples of new QES potentials are considered.