Dynamical symmetries of the Klein–Gordon equation Available to Purchase

The dynamical symmetries of the two-dimensional Klein–Gordon equations with equal scalar and vector potentials (ESVPs) 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.