A Gaussian wave packet method for studying time dependent quantum mechanics in a curve crossing system: Low energy motion, tunneling, and thermal dissipation

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Abstract
We explore numerically the behavior of a method of describing the time dependent quantum mechanics of a curve crossing system. The two nuclear wave functions corresponding to the two electronic states are each described by a Gaussian wave packet. The packet describing the incident state mimics the initial wave function, and the other packet is created by the time dependent Schrödinger equation. They are both propagated by using a variational method. The packets interact and we do not assume that they have a small width. Exploratory calculations are made for curve crossing dynamics at low kinetic energy above the barrier of the lowest adiabatic state, for tunneling, for multiple crossings, and for a curve crossing system which is strongly coupled to a harmonic bath whose motion is described by a mean trajectory classical Langevin method.

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