Higher-Order WKB Approximations for Relativistic Radial Problems in a Coulomb Field Author: Jeng-Yih Su

Abstract：

High-order WKB approximations for radial problems are applied to the Dirac-Coulomb radial equations in certain representation and to the Klein-Gordon radial equation for a Coulomb field. By requiring that the behavior of the total WKB wave function near the origin be the same as that of the exact wave function and by studying the WKB wave functions of any arbitrary orders, we obtain the exact energy spectrum for both cases in similar fashion as one obtains the exact spectrum for the Schrodinger radial equation for a Coulomb field. We also make some comments on the Langer-Kemble modification in the usual WKB approximation and on the Sommerfeld old quantum theory of a relativistic particle.

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