$δ$-Function Perturbations and Boundary Problems by Path Integration

Details $δ$-Function Perturbations and Boundary Problems by Path Integration $δ$-Function Perturbations and Boundary Problems by Path Integration

1993-02-13

arxiv.org/abs/hep-th/9302055v1

Annalen Phys. 2 (1993) 557-589

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1002/andp.19935050606

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.

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