Abstract:As a model for the semiclassical analysis of quantum-mechanical systems with both potentials and boundary conditions, we construct the WKB propagator for a linear potential sloping away from an impenetrable boundary. First, we find all classical paths from point y to point x in time t and calculate the corresponding action and amplitude functions. A large part of space-time turns out to be classically inaccessible, and the boundary of this region is a caustic of an unusual type, where the amplitude vanishes in… Show more
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