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Three one-dimensional quantum particles scattering problem with short-range repulsive pair potentials. To the question of absolutely continuous spectrum eigenfunctions asymptotics justification. / Budylin, Alexander M.; Levin, Sergei B.

Proceedings of the International Conference Days on Diffraction, DD 2016. ред. / A.Ya. Kazakov; A.P. Kiselev; O.V. Motygin; A.S. Kirpichnikova; L.I. Goray; P.V. Kapitanova. Institute of Electrical and Electronics Engineers Inc., 2016. стр. 95-100 7756821 (Proceedings of the International Conference Days on Diffraction, DD 2016).

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Harvard

Budylin, AM & Levin, SB 2016, Three one-dimensional quantum particles scattering problem with short-range repulsive pair potentials. To the question of absolutely continuous spectrum eigenfunctions asymptotics justification. в AY Kazakov, AP Kiselev, OV Motygin, AS Kirpichnikova, LI Goray & PV Kapitanova (ред.), Proceedings of the International Conference Days on Diffraction, DD 2016., 7756821, Proceedings of the International Conference Days on Diffraction, DD 2016, Institute of Electrical and Electronics Engineers Inc., стр. 95-100, 2016 International Conference Days on Diffraction, DD 2016, St. Petersburg, Российская Федерация, 27/06/16. https://doi.org/10.1109/DD.2016.7756821

APA

Budylin, A. M., & Levin, S. B. (2016). Three one-dimensional quantum particles scattering problem with short-range repulsive pair potentials. To the question of absolutely continuous spectrum eigenfunctions asymptotics justification. в A. Y. Kazakov, A. P. Kiselev, O. V. Motygin, A. S. Kirpichnikova, L. I. Goray, & P. V. Kapitanova (Ред.), Proceedings of the International Conference Days on Diffraction, DD 2016 (стр. 95-100). [7756821] (Proceedings of the International Conference Days on Diffraction, DD 2016). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/DD.2016.7756821

Vancouver

Budylin AM, Levin SB. Three one-dimensional quantum particles scattering problem with short-range repulsive pair potentials. To the question of absolutely continuous spectrum eigenfunctions asymptotics justification. в Kazakov AY, Kiselev AP, Motygin OV, Kirpichnikova AS, Goray LI, Kapitanova PV, Редакторы, Proceedings of the International Conference Days on Diffraction, DD 2016. Institute of Electrical and Electronics Engineers Inc. 2016. стр. 95-100. 7756821. (Proceedings of the International Conference Days on Diffraction, DD 2016). https://doi.org/10.1109/DD.2016.7756821

Author

Budylin, Alexander M. ; Levin, Sergei B. / Three one-dimensional quantum particles scattering problem with short-range repulsive pair potentials. To the question of absolutely continuous spectrum eigenfunctions asymptotics justification. Proceedings of the International Conference Days on Diffraction, DD 2016. Редактор / A.Ya. Kazakov ; A.P. Kiselev ; O.V. Motygin ; A.S. Kirpichnikova ; L.I. Goray ; P.V. Kapitanova. Institute of Electrical and Electronics Engineers Inc., 2016. стр. 95-100 (Proceedings of the International Conference Days on Diffraction, DD 2016).

BibTeX

@inproceedings{f32486afbabe40799ca9534d8194dd59,
title = "Three one-dimensional quantum particles scattering problem with short-range repulsive pair potentials. To the question of absolutely continuous spectrum eigenfunctions asymptotics justification",
abstract = "We consider the quantum scattering problem of three one-dimensional particles with repulsive shortrange pair potentials. For clarity, we restrict ourself by the case of finite pair potentials. The absence of singular continuous spectrum of the corresponding Schr{\"o}edinger operator for a broad class of pair potentials was proved earlier in a known work of E. Mourre. Nevertheless, the Mourre techniques do not allow description of the asymptotics of absolutely continuous spectrum eigenfunctions. In this work, regardless of Mourre results, we prove the existence of the resolvent limit values on absolutely continuous spectrum and construct them explicitly. It allows us, following the known procedure, to derive the absolutely continuous spectrum eigen-functions asymptotics, suggested earlier in works of V. S. Buslaev and his co-authors. Our approach, close to the foundational work of L. D. Faddeev devoted to three-dimensional particles, specifically uses the ideas of Schwarz alternating method.",
author = "Budylin, {Alexander M.} and Levin, {Sergei B.}",
note = "Publisher Copyright: {\textcopyright} 2016 IEEE.; 2016 International Conference Days on Diffraction, DD 2016 ; Conference date: 27-06-2016 Through 01-07-2016",
year = "2016",
month = nov,
day = "28",
doi = "10.1109/DD.2016.7756821",
language = "English",
series = "Proceedings of the International Conference Days on Diffraction, DD 2016",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "95--100",
editor = "A.Ya. Kazakov and A.P. Kiselev and O.V. Motygin and A.S. Kirpichnikova and L.I. Goray and P.V. Kapitanova",
booktitle = "Proceedings of the International Conference Days on Diffraction, DD 2016",
address = "United States",

}

RIS

TY - GEN

T1 - Three one-dimensional quantum particles scattering problem with short-range repulsive pair potentials. To the question of absolutely continuous spectrum eigenfunctions asymptotics justification

AU - Budylin, Alexander M.

AU - Levin, Sergei B.

N1 - Publisher Copyright: © 2016 IEEE.

PY - 2016/11/28

Y1 - 2016/11/28

N2 - We consider the quantum scattering problem of three one-dimensional particles with repulsive shortrange pair potentials. For clarity, we restrict ourself by the case of finite pair potentials. The absence of singular continuous spectrum of the corresponding Schröedinger operator for a broad class of pair potentials was proved earlier in a known work of E. Mourre. Nevertheless, the Mourre techniques do not allow description of the asymptotics of absolutely continuous spectrum eigenfunctions. In this work, regardless of Mourre results, we prove the existence of the resolvent limit values on absolutely continuous spectrum and construct them explicitly. It allows us, following the known procedure, to derive the absolutely continuous spectrum eigen-functions asymptotics, suggested earlier in works of V. S. Buslaev and his co-authors. Our approach, close to the foundational work of L. D. Faddeev devoted to three-dimensional particles, specifically uses the ideas of Schwarz alternating method.

AB - We consider the quantum scattering problem of three one-dimensional particles with repulsive shortrange pair potentials. For clarity, we restrict ourself by the case of finite pair potentials. The absence of singular continuous spectrum of the corresponding Schröedinger operator for a broad class of pair potentials was proved earlier in a known work of E. Mourre. Nevertheless, the Mourre techniques do not allow description of the asymptotics of absolutely continuous spectrum eigenfunctions. In this work, regardless of Mourre results, we prove the existence of the resolvent limit values on absolutely continuous spectrum and construct them explicitly. It allows us, following the known procedure, to derive the absolutely continuous spectrum eigen-functions asymptotics, suggested earlier in works of V. S. Buslaev and his co-authors. Our approach, close to the foundational work of L. D. Faddeev devoted to three-dimensional particles, specifically uses the ideas of Schwarz alternating method.

UR - http://www.scopus.com/inward/record.url?scp=85007044947&partnerID=8YFLogxK

U2 - 10.1109/DD.2016.7756821

DO - 10.1109/DD.2016.7756821

M3 - Conference contribution

T3 - Proceedings of the International Conference Days on Diffraction, DD 2016

SP - 95

EP - 100

BT - Proceedings of the International Conference Days on Diffraction, DD 2016

A2 - Kazakov, A.Ya.

A2 - Kiselev, A.P.

A2 - Motygin, O.V.

A2 - Kirpichnikova, A.S.

A2 - Goray, L.I.

A2 - Kapitanova, P.V.

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2016 International Conference Days on Diffraction, DD 2016

Y2 - 27 June 2016 through 1 July 2016

ER -

ID: 7592005