Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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).Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференций › статья в сборнике материалов конференции › научная › Рецензирование
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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