Complex semiclassical paths in the Feynman path integral for step potentials can be organized into equivalence classes, and one unsuppressed class provides the instanton mechanism for quantum reflection.
Path Integration Via Summation of Perturbation Expansions and Applications to Totally Reflecting Boundaries, and Potential Steps
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abstract
The path integral for the propagator is expanded into a perturbation series, which can be exactly summed in the case of $\delta$-function perturbations giving a closed expression for the (energy-dependent) Green function. Making the strength of the $\delta$-function perturbation infinite repulsive, produces a totally reflecting boundary, hence giving a path integral solution in half-spaces in terms of the corresponding Green function. The example of the Wood-Saxon potential serves by an appropriate limiting procedure to obtain the Green function for the step-potential and the finite potential-well in the half-space, respectively.
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2025 1verdicts
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The real-time Feynman path integral for step potentials
Complex semiclassical paths in the Feynman path integral for step potentials can be organized into equivalence classes, and one unsuppressed class provides the instanton mechanism for quantum reflection.