A Modified WKB Approximation for Phase Shifts

Abstract

Extending an idea of Good, a modified WKB approximation using radial wavefunctions having the form of free-particle solutions to the radial wave equation rather than an exponential form is developed. The lowest-order phase shifts are the same as those of the usual WKB approximation, but are improved by the contribution of the next order. The method is applied to two examples: the radial Dirac equation in the high-energy limit and the radial Schrödinger equation.