New conditionally exactly solvable inverse power law potentials

TL;DR

This paper introduces two new conditionally exactly solvable inverse power law potentials in quantum mechanics, highlighting their mathematical properties and solution methods involving hypergeometric functions.

Contribution

It presents novel partner potentials that are multiplicative shape invariant and provides a method to solve their Schrödinger equations explicitly.

Findings

Solutions involve sums of two confluent hypergeometric functions

Potentials are partner and multiplicative shape invariant

Properties of these potentials are analyzed

Abstract

We give two conditionally exactly solvable inverse power law potentials whose linearly independent solutions include a sum of two confluent hypergeometric functions. We notice that they are partner potentials and multiplicative shape invariant. The method used to find the solutions works with the two Schrodinger equations of the partner potentials. Furthermore we study some of the properties of these potentials.