A new class of exactly-solvable potentials by means of the hypergeometric equation

TL;DR

This paper introduces a new class of exactly-solvable quantum potentials derived from the hypergeometric equation, expanding the set of solvable models and enabling the construction of complex PT-invariant potentials.

Contribution

The authors present a novel class of exactly-solvable potentials distinct from Bose and Natanzon potentials, utilizing the hypergeometric equation and extending to PT-invariant potentials.

Findings

New class of exactly-solvable potentials derived from hypergeometric equation

Construction of complex PT-invariant potentials from the new class

Method applicable to other Fuchsian equations

Abstract

We obtained a new class of exactly-solvable potentials by means of the hypergeometric equation for Schrodinger equation, which different from the exactly-solvable potentials introduced by Bose and Natanzon. Using the new class of solvable potentials, we can obtain the corresponding complex PT-invariant potentials. This method can also apply to the other Fuchs equations.