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

摘要

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