The Faddeev equation and location of the essential spectrum of a three-particle model operator

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

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  5. 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.
  6. 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.
  7. Расулов Т. Х. Асимптотика дискретного спектра одного модельного оператора, ассоциированного с системой трёх частиц на решётке // ТМФ, 2010. Т. 163, № 1. С. 34-44.
  8. Фаддеев Л. Д. Математические вопросы квантовой теории рассеяния для системы трёх

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