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

T. Shivalingaswamy; B. A. Kagali

T. Shivalingaswamy Government College for Women
B. A. Kagali Bangalore University

Abstract

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.

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