Dynamical symmetries of the Klein-Gordon equation

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.

arXiv comment4 p

References in corpus (7)

• Pseudo-spin as a Relativistic Symmetry
• Dirac and Klein-Gordon equations with equal scalar and vector potentials
• Spin symmetry in the anti-nucleon spectrum
• Relativistic Harmonic Oscillator with Spin Symmetry
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Cited by in corpus (6)

• Pseudospin symmetry in single particle resonances in spherical square wells
• Higgs algebraic symmetry in the two-dimensional Dirac equation
• Comparison theorems for the Dirac equation with spin-symmetric and pseudo-spin-symmetric interactions
• New solutions of the D-dimensional Klein-Gordon equation via mapping onto the nonrelativistic one-dimensional Morse potential
• Quadratic Algebra Approach to Relativistic Quantum Smorodinsky-Winternitz Systems
• Generalized Virial Identities: Radial Constraints for Solitons, Instantons, and Bounces