Relativistic harmonic oscillator with spin symmetry

The eigenfunctions and eigenenergies for a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials are derived. Equal scalar and vector potentials may be applicable to the spectrum of an antinucleon embedded in a nucleus. Triaxial, axially deformed, and spherical oscillator potentials are considered. The spectrum has a spin symmetry for all cases and, for the spherical harmonic oscillator potential, a higher symmetry analogous to the SU(3) symmetry of the nonrelativistic harmonic oscillator is discussed.