Path integrals for potential problems with δ-function perturbation
- 21 November 1990
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 23 (22) , 5205-5234
- https://doi.org/10.1088/0305-4470/23/22/013
Abstract
The author presents several examples of potential problems with a δ-function perturbation by means of path integrals. The idea is to sum a perturbation series expansion resulting in an energy-dependent Green function G(E). The energy levels En of the perturbed problem are determined by the equation (one-dimensional case) iG(V)(a, a; En)=/ gamma where G(V) is the Green function of the unperturbed problem, gamma is the strength of the δ potential and a its location in R. In D-dimensional radial problems with a spherically shaped delta function located at r=a this equation changes into iG(V)l(a, a; En)=/aD-1 γ , where l denotes the angular momentum number.Keywords
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