Resolvent Operator Transformations and Bound-State Solutions for Confluent Natanzon Potentials

TL;DR

This paper introduces an algebraic approach to construct confluent Natanzon potentials with position-dependent mass by linking the resolvent operator to the Schrödinger equation, enabling new bound-state solutions.

Contribution

It presents a novel algebraic method that connects the resolvent operator to position-dependent mass Schrödinger equations for constructing specific potentials.

Findings

Derived explicit forms of confluent Natanzon potentials with position-dependent mass.

Established a relationship between the resolvent operator and the Schrödinger equation.

Facilitated the construction of bound-state solutions for these potentials.

Abstract

An algebraic method of constructing the confluent Natanzon potentials endowed with position-dependent mass is presented. This is possible by identifying the scaling resolvent operator (Green's function) to nonrelativistic position-dependent mass Schrodinger equation.