$\delta$-Function Perturbations and Boundary Problems by Path Integration

Abstract

A wide class of boundary problems in quantum mechanics is discussed by using path integrals. This includes motion in half-spaces, radial boxes, rings, and moving boundaries. As a preparation the formalism for the incorporation of $\delta$-function perturbations is outlined, which includes the discussion of multiple $\delta$-function perturbations, $\delta$-function perturbations along perpendicular lines and planes, and moving $\delta$-function perturbations. The limiting process, where the strength of the $\delta$-function perturbations gets infinite repulsive, has the effect of producing impenetrable walls at the locations of the $\delta$-function perturbations, i.e.\ a consistent description for boundary problems with Dirichlet boundary-condition emerges. Several examples illustrate the formalism.

35 pages, amstex, preprint SISSA/18/93/FM

References in corpus (3)

• Path Integral Solution of a Class of Explicitly Time-Dependent Potentials
• The Functional Integral for a Free Particle on a Half-Plane
• Classification of Solvable Feynman Path Integrals

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