Pseudospin symmetry and the relativistic ring-shaped non-spherical harmonic oscillator

A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The eigenfunctions and eigenenergies are obtained for the ring-shaped non-spherical harmonic oscillator by solving Dirac equation with equal mixture of vector and scalar potentials in opposite signs, for which pseudospin symmetry is exact. Several particular cases such as the ring-shaped harmonic oscillator, non-spherical harmonic oscillator, and spherical harmonic oscillator are also discussed.