To the Question on the Resolvent Kernel Asymptotics in the Three-Body Scattering Problem

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To the Question on the Resolvent Kernel Asymptotics in the Three-Body Scattering Problem. / Budylin, A. M.; Levin, S. B.

в: Journal of Mathematical Sciences (United States), Том 224, № 1, 01.07.2017, стр. 63-68.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{871ed8c471a2463ea5c433e82b5e6603,

title = "To the Question on the Resolvent Kernel Asymptotics in the Three-Body Scattering Problem",

abstract = "The present paper aims at announcing a new approach to the construction of the asymptotics (at infinity in configuration space) of the resolvent kernel of the Schr{\"o}dinger operator in the scattering problem of three one-dimensional quantum particles interacting by compactly supported pair repulsive potentials. Within the framework of this approach, the asymptotics of eigenfunctions of the absolutely continuous spectrum of the Schr{\"o}dinger operator can be constructed explicitly. It should be emphasized that the restriction of the consideration to the case of compactly supported pair potentials does not lead to a simplification of the problem in its essence, since the potential of the interaction of all three particles remains nondecreasing at infinity, but allows one to put aside a certain number of technical details.",

author = "Budylin, {A. M.} and Levin, {S. B.}",

note = "Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media New York.",

year = "2017",

month = jul,

day = "1",

doi = "10.1007/s10958-017-3394-4",

language = "English",

volume = "224",

pages = "63--68",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - To the Question on the Resolvent Kernel Asymptotics in the Three-Body Scattering Problem

AU - Budylin, A. M.

AU - Levin, S. B.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - The present paper aims at announcing a new approach to the construction of the asymptotics (at infinity in configuration space) of the resolvent kernel of the Schrödinger operator in the scattering problem of three one-dimensional quantum particles interacting by compactly supported pair repulsive potentials. Within the framework of this approach, the asymptotics of eigenfunctions of the absolutely continuous spectrum of the Schrödinger operator can be constructed explicitly. It should be emphasized that the restriction of the consideration to the case of compactly supported pair potentials does not lead to a simplification of the problem in its essence, since the potential of the interaction of all three particles remains nondecreasing at infinity, but allows one to put aside a certain number of technical details.

AB - The present paper aims at announcing a new approach to the construction of the asymptotics (at infinity in configuration space) of the resolvent kernel of the Schrödinger operator in the scattering problem of three one-dimensional quantum particles interacting by compactly supported pair repulsive potentials. Within the framework of this approach, the asymptotics of eigenfunctions of the absolutely continuous spectrum of the Schrödinger operator can be constructed explicitly. It should be emphasized that the restriction of the consideration to the case of compactly supported pair potentials does not lead to a simplification of the problem in its essence, since the potential of the interaction of all three particles remains nondecreasing at infinity, but allows one to put aside a certain number of technical details.

UR - http://www.scopus.com/inward/record.url?scp=85019627497&partnerID=8YFLogxK

U2 - 10.1007/s10958-017-3394-4

DO - 10.1007/s10958-017-3394-4

M3 - Article

AN - SCOPUS:85019627497

VL - 224

SP - 63

EP - 68

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -

ID: 9227185