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Path integrals for two‐ and three‐dimensional δ‐function perturbations
Author(s) -
Grosche Christian
Publication year - 1994
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.19945060406
Subject(s) - path integral formulation , formalism (music) , regularization (linguistics) , mathematics , mathematical physics , physics , mathematical analysis , quantum mechanics , computer science , quantum , art , musical , artificial intelligence , visual arts
The incorporation of two‐ and three‐dimensional Δ‐function perturbations into the path integral formalism is discussed. Contrary to the one‐dimensional case, a regularization prescription is needed due to the divergence of the Green function corresponding to a potential V , G ( v ) (x,y; E ) (x, y ϵ ℝ 2 , ℝ 3 ) for x → y . The known procedure to define proper self‐adjoint extensions for Hamiltonians with point‐interactions can be exploited to define the incorporation of δ‐function perturbations in the path integral. Several examples illustrate the formalism.