  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 antinucleion imbedded
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 non-relativistic harmonic oscillator is discussed.
