On the Discrete Spectrum of the Three-Particle Schrödinger Operator on a Two-Dimensional Lattice

We consider Schrödinger operator corresponding to the Hamiltonian of a system of three arbitrary particles on the two-dimensional lattice, where the particles interact pairwise via zero-range (contact) attractive potentials. We prove that the discrete spectrum of the Schrödinger operator is infinite...

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Bibliographic Details
Published in:	Lobachevskii journal of mathematics Vol. 43; no. 11; pp. 3239 - 3251
Main Authors:	Muminov, Z. I., Aliev, N. M., Radjabov, T.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-11-2022 Springer Nature B.V
Subjects:	Algebra Analysis Contact potentials Geometry Mathematical Logic and Foundations Mathematics Mathematics and Statistics Operators (mathematics) Probability Theory and Stochastic Processes cluster operators essential spectrum dispersion functions Schrödinger operator discrete spectrum bound states zero-range pair potentials
Online Access:	Get full text
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Summary:	We consider Schrödinger operator corresponding to the Hamiltonian of a system of three arbitrary particles on the two-dimensional lattice, where the particles interact pairwise via zero-range (contact) attractive potentials. We prove that the discrete spectrum of the Schrödinger operator is infinite, if the masses of two particles in a three-particle system are infinite.
ISSN:	1995-0802 1818-9962
DOI:	10.1134/S1995080222140268