Theory of Semiclassical Transition Probabilities (S Matrix) for Inelastic and Reactive Collisions. III. Uniformization Using Exact Trajectories

Abstract

A canonical transformation of coordinates in Part I is made using exact trajectories. The transformation tends to uniformize all coordinates including that for the radial motion, thus removing the singularities in the simple semiclassical exponential wavefunction in typical cases. The new coordinates are "time" and certain constants of the motion. A symmetrical choice for the transformation then yields an integral expression for the S matrix satisfying the principle of microscopic reversibility. Topics discussed include semiclassical unitary transformations and time‐reversal properties of action‐angle variables and of semi‐classical wavefunctions. Applications and numerical tests of the integral expression for S_(mn) are in progress.

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