Generalization of the Modified WKB Approximation for Phase Shifts

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Abstract
A generalization of the modified WKB method proposed by Good and by Rosen and Yennie as applied to the scattering problem is presented. In the formulation of this problem the main equation connects two parts, the solved part and the part to be solved. We consider not only the case where the radical wave function of the solved part has the form of the three-dimensional free-particle solution, as is done by the authors mentioned above, but also where it has the form given by an explicit solution with a known potential. The closer the resemblance between the potentials of the unsolved and the solved parts, the better the result is.

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