On the Essential Spectrum of Three-Particle Discrete Schrödinger Operators with Short-Range Potentials
Z. E. MuminovSamarkand Branch, Institute of Mathematics Named After V. I. Romanovsky, 140104, Samarkand, UzbekistanSh. S. LakaevUzbek-Israel Joint Faculty, National University of Uzbekistan, 100174, Tashkent, UzbekistanN. M. AlievDepartment of Scientific Research, National University of Uzbekistan, 100174, Tashkent, Uzbekistan
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Annotatsiya
We investigate a family of Schrödinger operators $$H(K)$$ , $$K\in(-\pi,\pi]^{d}$$ associated with a system of three quantum particles on the $$d$$ -dimensional lattice $${\mathbb{Z}}^{d}$$ interacting via short-range pair potentials. It’s shown that the essential spectrum of the three-particle discrete Schrödinger operator $$H(K)$$ , $$K\in(-\pi,\pi]^{d}$$ consists of a finitely many bounded closed intervals.
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