Boundary behavior of quantum Green's functions

L. Šamaj, J. K. Percus, P. Kalinay

Research output: Contribution to journalArticle

Abstract

We consider the time-independent Green's function for the Schrödinger operator with a one-particle potential, defined in a d-dimensional domain. Recently, in one dimension (ID), the Green's function problem was solved explicitly in inverse form, with diagonal elements of the Green's function as prescribed variables. In this article, the ID inverse solution is used to derive leading behavior of the Green's function close to the domain boundary. The emphasis is put onto "universal" expansion terms which are dominated by the boundary and do not depend on the particular shape of the applied potential. The inverse formalism is extended to higher dimensions, especially to 3D, and subsequently the boundary form of the Green's function is predicted for an arbitrarily shaped domain boundary.

Original languageEnglish (US)
Pages (from-to)1625-1637
Number of pages13
JournalJournal of Mathematical Physics
Volume44
Issue number4
DOIs
StatePublished - Apr 1 2003

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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