Dynamical symmetries of the Klein-Gordon equation

TL;DR

This paper investigates the dynamical symmetries of the two-dimensional Klein-Gordon equation with equal scalar and vector potentials, deriving symmetry generators and energy spectra on plane and spherical geometries.

Contribution

It identifies and constructs the symmetry groups and algebraic structures for Klein-Gordon systems with specific potentials, providing a unified approach to their energy levels.

Findings

Derived SO(3) and SU(2) symmetry generators for Coulomb and harmonic oscillator potentials.

Constructed the Higgs algebra on the sphere.

Obtained energy spectra using Casimir operators.

Abstract

The dynamical symmetries of the two-dimensional Klein-Gordon equations with equal scalar and vector potentials (ESVP) are studied. The dynamical symmetries are considered in the plane and the sphere respectively. The generators of the SO(3) group corresponding to the Coulomb potential, and the SU(2) group corresponding to the harmonic oscillator potential are derived. Moreover, the generators in the sphere construct the Higgs algebra. With the help of the Casimir operators, the energy levels of the Klein-Gordon systems are yielded naturally.