Semiclassical S-matrix theory. VI. Integral expression and transformation of conventional coordinates

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Abstract
Sometimes, as in reactive systems, action‐angle variables are not conveniently defined at all points of the trajectory and recourse must be made to conventional coordinates. A simple canonical transformation converts the latter to coordinates of which one is time and the remainder are constant along the trajectory. The transformation serves to remove the singularities of the semiclassical wavefunction at the turning points of the trajectory. It yields, thereby, an integral expression for the S matrix by having produced wavefunctions which can be integrated over all space. The result supplements that of Paper III [R. A. Marcus, J. Chem. Phys. 56, 311 (1972)], which was derived for systems for which action‐angle variables could be defined throughout the collision.