Boundary behavior of quantum Green's functions

L. Šamaj, Jerome 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

Fingerprint

Boundary Behavior
Green's function
Green's functions
One Dimension
Higher Dimensions
formalism
operators
expansion
Term
Operator

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

Cite this

Boundary behavior of quantum Green's functions. / Šamaj, L.; Percus, Jerome; Kalinay, P.

In: Journal of Mathematical Physics, Vol. 44, No. 4, 01.04.2003, p. 1625-1637.

Research output: Contribution to journalArticle

Šamaj, L, Percus, J & Kalinay, P 2003, 'Boundary behavior of quantum Green's functions', Journal of Mathematical Physics, vol. 44, no. 4, pp. 1625-1637. https://doi.org/10.1063/1.1557330
Šamaj, L. ; Percus, Jerome ; Kalinay, P. / Boundary behavior of quantum Green's functions. In: Journal of Mathematical Physics. 2003 ; Vol. 44, No. 4. pp. 1625-1637.
@article{68bc261c29d04551a4a86b2fc9dbf32a,
title = "Boundary behavior of quantum Green's functions",
abstract = "We consider the time-independent Green's function for the Schr{\"o}dinger 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.",
author = "L. Šamaj and Jerome Percus and P. Kalinay",
year = "2003",
month = "4",
day = "1",
doi = "10.1063/1.1557330",
language = "English (US)",
volume = "44",
pages = "1625--1637",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics Publising LLC",
number = "4",

}

TY - JOUR

T1 - Boundary behavior of quantum Green's functions

AU - Šamaj, L.

AU - Percus, Jerome

AU - Kalinay, P.

PY - 2003/4/1

Y1 - 2003/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0344950415&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0344950415&partnerID=8YFLogxK

U2 - 10.1063/1.1557330

DO - 10.1063/1.1557330

M3 - Article

AN - SCOPUS:0344950415

VL - 44

SP - 1625

EP - 1637

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 4

ER -