Abstract
A new trajectory-based method of transition probability evaluation in quantum system was developed. It is based on a path integral representation of probability and uses Weyl symbols for initial and final states. The method belongs to the efficient initial value representation (IVR) schemes. The pre-exponential factor specific to the semi-classical method is equal to one, and does not need be separately calculated. This eliminates problems with caustics and Maslov indices of trajectories. The method is equally efficient for evaluation of the transition probabilities into separate states and groups of states, including an entire ionization continuum, for example. The capabilities of the method are demonstrated by evaluation of photo-excitation and photo-ionization probabilities in the hydrogen atom exposed to an ultrashort photo-pulse, and total photo-ionization probability in the helium atom.
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