Abstract
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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This work was partially supported by the Grant OT–F4–66 of Fundamental Science Foundation of Uzbekistan.
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(Submitted by T. K. Yuldashev)
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Muminov, Z.E., Lakaev, S.S. & Aliev, N.M. On the Essential Spectrum of Three-Particle Discrete Schrödinger Operators with Short-Range Potentials. Lobachevskii J Math 42, 1304–1316 (2021). https://doi.org/10.1134/S1995080221060196
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DOI: https://doi.org/10.1134/S1995080221060196