Proper incorporation of self-adjoint extension method to Green's function formalism : one-dimensional ${\delta }^{{}^{\prime }}$-function potential case

Abstract

One-dimensional ${\delta }^{{}^{\prime }}$-function potential is discussed in the framework of Green's function formalism without invoking perturbation expansion. It is shown that the energy-dependent Green's function for this case is crucially dependent on the boundary conditions which are provided by self-adjoint extension method. The most general Green's function which contains four real self-adjoint extension parameters is constructed. Also the relation between the bare coupling constant and self-adjoint extension parameter is derived.

LATEX, 13 pages

References in corpus (3)

• Path integral treatment of two- and three-dimensional delta-function potentials and application to spin-1/2 Aharonov-Bohm problem
• ${\delta }^{\prime }$-Function Perturbations and Neumann Boundary-Conditions by Path Integration
• Path Integral Discussion of Two and- Three-Dimensional $\delta$-Function Perturbations

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