EXACT SOLUTION OF DIRAC EQUATION WITH AN EQUIVALENT OSCILLATOR POTENTIAL

It is shown that a Hamiltonian obtained by adding an energy term λ2ρ2σ•rK|σ•L+1|-1 to the free-particle Dirac Hamiltonian possesses exact solutions and a discrete spectrum of high degeneracy. In the nonrelativistic limit this leads to an isotropic harmonic oscillator with a spin-orbit coupling term of the Thomas-Frenkel form. The symmetry is likely to be at least as high as SU3. © 1969 The American Physical Society.