Algebraic approach for shape invariant potentials in Klein-Gordon equation

TL;DR

This paper explores an algebraic approach to shape invariant potentials within the Klein-Gordon equation, revealing finite-dimensional algebraic structures for certain physical potentials under specific conditions.

Contribution

It introduces a method to derive finite-dimensional algebraic structures for shape invariant potentials in the Klein-Gordon equation, expanding the algebraic framework for relativistic quantum systems.

Findings

Finite-dimensional algebraic structures are obtained for specific potentials.

The method applies to s-wave Klein-Gordon equation with scalar and vector potentials.

Shape invariance conditions lead to algebraic simplifications.

Abstract

The Shape invariant method has the algebraic structure and its algebras are infinite-dimensional. These algebras are converted into finite-dimensional under conditions. Based on the property of this method we obtain the algebraic structure of some physical potentials in the s-wave Klein-Gordon equation with scalar and vector potential which satisfy the Shape invariant condition.