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δ‐function perturbations and boundary problems by path integration
Author(s) -
Grosche C.
Publication year - 1993
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19935050606
Subject(s) - dirac delta function , physics , limiting , formalism (music) , boundary value problem , path integral formulation , dirichlet boundary condition , classical mechanics , function (biology) , perpendicular , boundary (topology) , mathematical analysis , mathematical physics , quantum , mathematics , quantum mechanics , geometry , evolutionary biology , engineering , visual arts , mechanical engineering , art , musical , biology
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.