Improved solutions to the equation of motion in the uniform WKB theory for two‐channel problems

Abstract

The equation of motion in the uniform WKB theory for a two‐channel problem is reinvestigated in order to obtain improved approximate solutions that would perform better than the first order Magnus approximation solution previously used in the analysis of two‐channel inelastic collision problems. We have developed two approximate solutions and investigated their variants in the paper. The two main improved approximate solutions are obtained by properly resumming the Magnus expansion in a novel way and also by appropriately modifying the equation of motion such that the Magnus approximation used on it would not damage the accuracy of the solution thus obtained. The solutions obtained give rise to transition probabilities well comparable over a wide range of the coupling constant with those obtained by the numerical solution of the coupled Schrödinger equations.