Harmonic oscillator and nuclear pseudospin - Lisboa, Ronai; Malheiro, Manuel; De Castro, Antonio S. [UNESP]; Alberto, Pedro; Fiolhais, Manuel (AIP Publishing, 2004)
A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U, linear in r. Setting either Σ = S + V or Δ = V - S to zero, analytical solutions for bound states are found. The eingenenergies and their nonrelativistic limits are presented and particular cases are discussed, especially the case Σ = 0, for which pseudospin symmetry is exact.