Semiclassical theory of time-dependent curve crossing problems

It is shown that the newly completed accurate semiclassical theory for time-independent curve crossing problems can be usefully utilized to study various time-dependent curve crossing problems. Quadratic time-dependent problems can be solved exactly with use of the theory developed for the time-independent linear potential model. Furthermore, accurate and compact semiclassical theory can be formulated for general curved potentials. Even diabatically avoided crossing cases can be nicely treated. Multi-level problems can also be handled without difficulty with use of a new method to evaluate the necessary basic parameters directly from adiabatic potentials on the real axis in the fully diagonalized adiabatic representation. This method does not require a search for complex crossing points in the multi-level system, which is practically very difficult especially when the number of levels exceeds three. (C) 1997 American Institute of Physics.