Eigenenergies of a Relativistic Particle in an Infinite Range Linear Potential Using WKB Method.

摘要

Energy eigenvalues for a non-relativistic particle in a linear potential well are available. In this paper we obtain the eigenenergies for a relativistic spin less particle in a similar potential using an extension of the well-known WKB method treating the potential as the time component of a four-vector potential. Since genuine bound states do not exist for positive rising potentials, our calculations are valid only for fairly low-lying levels. The transcendental eigenvalue equation that is obtained is solved using Mathematica software to get eigenenergies. Our results are compared with those for the non relativistic case. The results may find applications besides having conceptual significance.