Mass Spectrum of Dirac Equation with Local Parabolic Potential

Abstract

In this paper, we solve the eigen solutions and mass strectra of the Dirac equation with local parabolic potential which is approximately equal to the short distance potential generated by spinor itself. The mass spectrum is quite different from that of a spinor in Coulomb potential. The masses of some baryons are similar to this one. The mass-angular momentum relation $m=m(J,n)$ is quite similar to the Regge trajectories. The parabolic potential has property of asymptotic freedom near the center and confinement at large distance. So the results imply that, the local parabolic potential may be more suitable for describing nuclear potential approximately. The solving procedure can also be used to solve the Dirac equation with other complicated potential.