# Ladder operators for the Ben Daniel-Duke Hamiltonians and their SUSY partners

## TL;DR

This paper develops ladder operators for Ben Daniel-Duke Hamiltonians with position-dependent mass, using supersymmetric transformations to analytically solve for eigenfunctions of generated Hamiltonians.

## Contribution

It introduces a method to construct ladder operators for position-dependent mass systems and applies SUSY transformations to find analytical solutions.

## Key findings

- Ladder operators can be constructed for Ben Daniel-Duke Hamiltonians.
- Supersymmetric transformations generate new Hamiltonians with known eigenfunctions.
- Analytical solutions are obtained for specific mass profiles.

## Abstract

Position dependent mass systems can be described by a class of operators which include the Ben Daniel-Duke Hamiltonians. The usual methods to solve this kind of problems are, in general, either numerical or those looking for a connection with constant mass problems. In this paper we impose the existence of first-order ladder operators to fix our initial system. Then, we perform the first and second order supersymmetric transformations to generate families of Hamiltonians whose eigenfunctions are known analytically for a given mass profile.