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Keywords:

  • Quantum mechanics;
  • Path integrals;
  • Boundary-problems

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 δ-function perturbations is outlined, which includes the discussion of multiple δ-function perturbations, δ-function perturbations along perpendicular lines and planes, and moving δ-function perturbations. The limiting process, where the strength of the δ-function perturbations gets infinitely repulsive, has the effect of producing impenetrable walls at the locations of the δ-function perturbations, i.e. a consistent description for boundary problems with Dirichlet boundary-condition emerges. Several examples illustrate the formalism.