A unified treatment of exactly solvable and quasi-exactly solvable quantum potentials

TL;DR

This paper introduces a unified algebraic approach using sl(2) symmetry to generate new exactly solvable and quasi-exactly solvable quantum potentials, expanding the class of solvable models in quantum mechanics.

Contribution

It presents a novel unified method leveraging hidden algebraic structures to systematically construct new solvable quantum potentials.

Findings

Two new classes of quasi-exactly solvable systems are identified.

One class is of periodic type, the other hyperbolic.

The approach unifies the treatment of exactly and quasi-exactly solvable potentials.

Abstract

By exploiting the hidden algebraic structure of the Schrodinger Hamiltonian, namely the sl(2), we propose a unified approach of generating both exactly solvable and quasi-exactly solvable quantum potentials. We obtain, in this way, two new classes of quasi-exactly solvable systems one of which is of periodic type while the other hyperbolic.