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Path integral treatment of two- and three-dimensional delta-function potentials and application to spin-1/2 Aharonov-Bohm problem

D. K. Park
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Abstract

Delta-function potentials in two- and three-dimensional quantum mechanics are analyzed by the incorporation of the self-adjoint extension method to the path integral formalism. The energy-dependent Green functions for free particle plus delta-function potential systems are explicitly calculated. Also the energy-dependent Green function for the spin-1/2 Aharonov-Bohm problem is evaluated. It is found that the only one special value of the self-adjoint extension parameter gives a well-defined and non-trivial time-dependent propagator. This special value corresponds to the viewpoint of the spin-1/2 Aharonov-Bohm problem when the delta-function is treated as a limit of the infinitesimal radius.

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D. K. Park. 1994-05-04. Path integral treatment of two- and three-dimensional delta-function potentials and application to spin-1/2 Aharonov-Bohm problem. https://doi.org/10.1063/1.531271

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