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Path Integration Via Summation of Perturbation Expansions and Applications to Totally Reflecting Boundaries, and Potential Steps

Christian Grosche
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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 $δ$-function perturbations giving a closed expression for the (energy-dependent) Green function. Making the strength of the $δ$-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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Christian Grosche. 1993-03-23. Path Integration Via Summation of Perturbation Expansions and Applications to Totally Reflecting Boundaries, and Potential Steps. https://doi.org/10.1103/physrevlett.71.1

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