Green’s-function approach to two- and three-dimensional delta-function potentials and application to the spin-1/2 Aharonov–Bohm problem

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Abstract
Delta-function potentials in two- and three-dimensional quantum mechanics are analyzed by incorporating the self-adjoint extension method within the Green's-function method. The energy-dependent Green's functions for free particle plus delta-function potential systems are explicitly determined and similar calculations are carried out for the spin-1/2 Aharonov-Bohm system. It is found that the time-dependent propagator for the latter cannot be evaluated analytically except for a particular value of the self-adjoint extension parameter. It corresponds to the case in which the singular solution alone contributes for the partial wave defined by \m+a\ < 1. (C) 1995 American Institute of Physics.
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