The Hierarchy of Hamiltonians for a Restricted Class of Natanzon Potentials

TL;DR

This paper explores a specific subset of Natanzon potentials using Supersymmetric Quantum Mechanics, explicitly constructing Hamiltonian hierarchies and proposing a general superpotential form.

Contribution

It introduces a hierarchy of Hamiltonians for a restricted class of Natanzon potentials and provides explicit evaluations and a general superpotential form.

Findings

Explicit Hamiltonian hierarchy constructed

General superpotential form proposed

First members of the superfamily explicitly evaluated

Abstract

The restricted class of Natanzon potentials with two free parameters is studied within the context of Supersymmetric Quantum Mechanics. The hierarchy of Hamiltonians is indicated, where the first members of the superfamily are explicitly evaluated and a general form for the superpotential is proposed.