New Solvable Potentials with Bound State Spectrum

TL;DR

This paper introduces a new family of exactly solvable quantum potentials linked to the Schroedinger-Riccati equation, expanding the class of solvable models and deriving a related nonlinear Schroedinger-type equation.

Contribution

It presents a novel, parameter-dependent class of solvable potentials related to hypergeometric functions and generalizes them to broader classes, also deriving a nonlinear Schroedinger-type equation.

Findings

New solvable potentials related to hypergeometric functions

Generalization to wider classes of solvable potentials

Derivation of a nonlinear Schroedinger-type equation

Abstract

A new family of solvable potentials related to the Schroedinger-Riccati equation has been investigated. This one-dimensional potential family depends on parameters and is restricted to the real interval. It is shown that this potential class, which is a rather general class of solvable potentials related to the hypergeometric functions, can be generalized to even wider classes of solvable potentials. As a consequence the nonlinear Schroedinger-type equation has been obtained.