Bound states for a kind of relativistic non-harmonic oscillator systems

Abstract

For a three-dimensional non-harmonic oscillator potential 12r2+A2r 2, the s-wave bound solutions of both Dirac equation and Klein-Gordon equation are giv en when the scalar potential is equal to the vector potential. We find that the radial component equations for both two-dimensional Dirac equation and three-dimensional one are the same when the scalar potential equals to the vector potenti al, and the corresponding s-wave bound solutions for the two-dimensional system are also obtained.