Van Vleck-Gutzwiller propagator

The evaluation of the semiclassical Van Vleck-Gutzwiller propagator (106) amounts to the solution of a boundary-value problem. That is, given a trajectory characterized by the position q(f) = q, and momentum p(f) = p, we need to hnd the roots of the equation = q floiPo)- To circumvent this cumbersome root search, one may rewrite the semiclassical expression for the transition amplitude (105) as an initial-value problem [104-111]... 

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