A Group-Theoretical Method for Natanzon Potentials in Position-Dependent Mass Background

TL;DR

This paper introduces a group-theoretical approach using conformal mappings to derive exact Natanzon potentials in systems with position-dependent mass, connecting algebraic methods with hypergeometric potentials.

Contribution

It presents a novel method leveraging su(1,1) algebra and conformal mappings to systematically derive Natanzon potentials with position-dependent mass.

Findings

Exact expressions for Natanzon potentials obtained

Method simplifies derivation of potentials in complex backgrounds

Connects algebraic and hypergeometric potential frameworks

Abstract

A new manner for deriving the exact potentials is presented. By making use of conformal mappings, the general expression of the effective potentials deduced under su(1,1) algebra can be brought back to the general Natanzon hypergeometric potentials.