Email this article The Faddeev equation and location of the essential spectrum of a three-particle model operator
- Authors: Rasulov T.K.1, Rakhmonov A.A2
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Affiliations:
- Bukhara State University, Physics and Mathematics Faculty
- University of Bern, Faculty of Science
- Issue: Vol 15, No 2 (2011)
- Pages: 170-180
- Section: Articles
- URL: https://journals.eco-vector.com/1991-8615/article/view/21027
- ID: 21027
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Abstract
In this paper a model operator H associated to a system of three-particles on a lattice is considered. The location of the essential spectrum of H is described by the spectrum of channel operators. The Faddeev type equation for the eigenvectors of H is obtained.
About the authors
Tulkin Kh Rasulov
Bukhara State University, Physics and Mathematics Faculty
Email: rth@mail.ru
(к.ф.-м.н., доц.), доцент, каф. алгебры и анализа1 ; докторант, математический институт2; Бухарский государственный университет, физико-математический факультет; Bukhara State University, Physics and Mathematics Faculty
Askar A Rakhmonov
University of Bern, Faculty of Science
Email: araxmonov@mail.ru
студент; Университет Берна, философско-научный факультет; University of Bern, Faculty of Science
References
- Reed M., Simon B. Methods of modern mathematical physics. Vol. IV: Analysis of operators. New York-London: Academic Press, 1978. 396 pp.
- Жислин Г. М. Исследование спектра оператора Шрёдингера для системы многих частиц // Труды Моск. мат. общ-ва, 1960. Т. 9. С. 81-120.
- Albeverio S., Lakaev S. N., Muminov Z. I. Schrödinger operators on lattices. The Efimov effect and discrete spectrum asymptotics // Ann. Henri Poincaré, 2004. Vol. 5, no. 4. Pp. 743-772.
- Albeverio S., Lakaev S. N., Muminov Z. I. On the structure of the essential spectrum for the three-particle Schrödinger operators on lattices // Math. Nachr., 2007. Vol. 280, no. 7. Pp. 699-716.
- Albeverio S., Lakaev S. N., Muminov Z. I. On the number of eigenvalues of a model operator associated to a system of three-particles on lattices // Russ. J. Math. Phys., 2007. Vol. 14, no. 4. Pp. 377-387.
- Albeverio S., Lakaev S. N., Djumanova R. Kh. The essential and discrete spectrum of a model operator associated to a system of three identical quantum particles // Reports on Math. Phys., 2009. Vol. 63, no. 3. Pp. 359-380.
- Расулов Т. Х. Асимптотика дискретного спектра одного модельного оператора, ассоциированного с системой трёх частиц на решётке // ТМФ, 2010. Т. 163, № 1. С. 34-44.
- Фаддеев Л. Д. Математические вопросы квантовой теории рассеяния для системы трёх
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