The “quantum trajectory” wavepacket approach to semiclassical collision dynamics is generalized to include effects which cause distortion of initially gaussian wavepackets. The generalization takes the form of a discrete phase space path “integral” or sum. A complete set of gaussian phase space localized basis functions is proposed, and in the semiclassical limit, each basis function time develops in a simple classical-like fashion. Thus, the formulation conveniently builds in the correct limiting semiclassical behavior. The phase space path sum is formally exact, numerically it appears convenient, and is apparently equally at home in quantum and semiclassical regimes.
In this paper, we propose and solve sequential coupling models for molecular dissociation of the Rice‐McLaughlin‐Jortner (RMJ) type in which the usual assumption of constant coupling among the states is replaced by an assumption of random coupling. The counter‐intuitive nonsequential branching behavior found previously for constant coupling is eliminated and we find completely sequential time dependence which obeys the phenomenological rate equations. We isolate the features of constant vs random coupling which give rise to the branching vs sequential behavior in terms of simple physical models and considerations of the coherence properties of the wavefunction. It is concluded that constant coupling is inappropriate for most molecules, and that the random coupling assumption has the effect of validating the use of a random phase approximation which in turn causes the molecule to decay as if each quasibound molecular level is coupled to its own continuum. Our conclusions do not change when we solve an extended model with many continua, with each molecular level coupled to each continuum.
The quantum mechanical collinear atom-diatom collision problem is treated via a discrete expansion of the wave-function in terms of uncoupled, distorte wave states, using the Wigner-Eisenbud R-matrix formalism. Previously unreported narrow Feshbach resonances, which reduce the inelastic transition probability, are easily found and examined. Off resonant transition probabilities are in agreement with the work of Diestler and Feuer using the same model.