Quesne-like ring-shaped spherical harmonic oscillator potential and pseudospin symmetry

A Quesne-like ring-shaped spherical harmonic oscillator potential is put foword and studied for spin 1/2 particles based on the Dirac equation， the Dirac Hamiltonian contains a scalar and a vector Quesne-like ring-shaped harmonic oscillator potentials. Setting Σ ＝ S ( r )+V( r )=0,we obtain the bound state solutions and eigenenergies with the two-component approach. The result shows the pseudospin symmetry exists in the Quesne-like ring-shaped harmonic oscillator potential. The general properties of both the ring-shaped spherical harmonic oscillator potential and the ring-shaped non-spherical harmonic oscillator potential are discussed.