Analytic Continuation of Classical Mechanics for Classically Forbidden Collision Processes

摘要: Classically forbidden processes are those that cannot take place via ordinary classical dynamics. Within the framework of S‐matrix theory, however, mechanics can be analytically continued and classical‐limit approximations obtained for these classically forbidden, or weak transition amplitudes (i.e., elements). The most powerful general way continuing a complex dynamical system is to integrate equations motion themselves through inaccessible regions phase space. Success in calculating trajectories reported this work; with certain special features complex‐valued recognized taken account of, it seen they essentially as easy deal numerically real) trajectories. Application linear A+BC collision (vibrational excitation) gives excellent results; probabilities small 10−11 (the smallest ones available comparison) have been obtained, agreement exact quantum mechanical values being within few percent.