Obtaining eigenvalues and solutions for a class of differential equations using Casimir operator

TL;DR

This paper introduces a group theoretic approach using spectrum generating algebras to compute eigenvalues of certain differential equations efficiently, avoiding explicit solutions and simplifying the process for specific potentials.

Contribution

It presents a novel method leveraging Casimir operators and spectrum generating algebras to determine eigenvalues of differential equations without direct solving.

Findings

Eigenvalues computed without explicit solutions

Method applicable to specific potential types

Simplifies solving differential equations using group theory

Abstract

Using the group theoretic method of spectrum generating algebras a class of differential equations is obtained whose eigenvalues are calculated without explicitly solving the equations. Solutions can be easily obtained by group theoretic methods for a certain type of potentials.