Analytic Continuation of Classical Mechanics for Classically Forbidden Collision Processes

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摘要：

Classically forbidden processes are those that cannot take place via ordinary classical dynamics. Within the framework of classicalS‐matrix theory, however, classical mechanics can be analytically continued and classical‐limit approximations obtained for these classically forbidden, or weak transition amplitudes (i.e.,S‐matrix elements). The most powerful and general way of analytically continuing classical mechanics for a complex dynamical system is to integrate the equations of motion themselves through the classically inaccessible regions of phase space. Success in calculating these analytically continued trajectories is reported in this work; with certain special features of these complex‐valued trajectories recognized and taken account of, it is seen that they are essentially as easy to deal with numerically as ordinary (i.e., real) classical trajectories. Application to the linear A+BC collision (vibrational excitation) gives excellent results; transition probabilities as small as 1011(the smallest ones available for comparison) have been obtained, agreement with the exact quantum mechanical values being within a few percent.

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Theoretical or Mathematical/ molecular collision processes S-matrix theory/ complex valued trajectories analytic continuation of classical mechanics classically forbidden collision processes S-matrix theory weak transition amplitudes equations of motion/ A1120 S-matrix theory A3370F Molecular lifetimes, absolute and relative line and band intensities A3420 Interatomic and intermolecular potentials and forces A3440 Elastic scattering of atoms and molecules A3450 Inelastic scattering of atoms and molecules