On the structure of the essential spectrum for discrete Schrödinger operators associated with three-particle system

Authors

Shukhrat Lakaev, National University of UzbekistanFollow
Tirkash Radjabov, Samarkand State UniversityFollow
Nizomiddin Makhmasaitovich Aliev, National University ofUzbekistan, TashkentFollow

Abstract

We consider a family of discrete Schrödinger operators $H(K),\,K\in (-\pi,\pi]^5$ associated with a system of three quantum particles on the five-dimensional lattice ${\mathbb{Z}}^5$ interacting via short-range pair potentials and having arbitrary "dispersion functions" with not necessarily compact support.

We show that the essential spectrum of the three-particle discrete Schr\"odinger operator $H(K),\,K\in (-\pi,\pi]^5$ consists of a finitely many bounded closed intervals.

First Page

104

Last Page

120

References

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Recommended Citation

Lakaev, Shukhrat; Radjabov, Tirkash; and Aliev, Nizomiddin Makhmasaitovich (2021) "On the structure of the essential spectrum for discrete Schrödinger operators associated with three-particle system," Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences: Vol. 4: Iss. 2, Article 4.
DOI: https://doi.org/10.56017/2181-1318.1139