M. I. Muminov, “The infiniteness of the number of eigenvalues in the gap in the essential spectrum for the three-particle Schrödinger operator on a lattice”, TMF, 159:2 (2009), 299–317; Theoret. and Math. Phys., 159:2 (2009), 667

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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 159, Number 2, Pages 299–317
DOI: https://doi.org/10.4213/tmf6350 (Mi tmf6350)

This article is cited in 15 scientific papers (total in 15 papers)

The infiniteness of the number of eigenvalues in the gap in the essential spectrum for the three-particle Schrödinger operator on a lattice

M. I. Muminov

A. Navoi Samarkand State University

Full-text PDF (498 kB) Citations (15)

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DOI: https://doi.org/10.4213/tmf6350

Abstract: We consider a system of three arbitrary quantum particles on a three-dimensional lattice that interact via attractive pair contact potentials. We find a condition for a gap to appear in the essential spectrum and prove that there are infinitely many eigenvalues of the Hamiltonian of the corresponding three-particle system in this gap.

Keywords: three-particle system on a lattice, Schrödinger operator, essential spectrum, discrete spectrum, compact operator.

Received: 14.02.2008
Revised: 22.08.2008

English version:
Theoretical and Mathematical Physics, 2009, Volume 159, Issue 2, Pages 667–683
DOI: https://doi.org/10.1007/s11232-009-0054-y

Bibliographic databases:

Language: Russian

Citation: M. I. Muminov, “The infiniteness of the number of eigenvalues in the gap in the essential spectrum for the three-particle Schrödinger operator on a lattice”, TMF, 159:2 (2009), 299–317; Theoret. and Math. Phys., 159:2 (2009), 667–683

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https://doi.org/10.4213/tmf6350

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This publication is cited in the following 15 articles:

M. I. Muminov, U. R. Shadiev, “On the Existence of an Eigenvalue of the Generalized Friedrichs Model”, Russ Math., 68:4 (2024), 28
N. M. Aliev, “Asymtotic of the Discrete Spectrum of the Three-Particle Schrödinger Operator on a One-Dimensional Lattice”, Lobachevskii J Math, 44:2 (2023), 491
Z. I. Muminov, N. M. Aliev, T. Radjabov, “On the Discrete Spectrum of the Three-Particle Schrödinger Operator on a Two-Dimensional Lattice”, Lobachevskii J Math, 43:11 (2022), 3239
J.I. Abdullaev, A.M. Khalkhuzhaev, “The existence of eigenvalues of Schrödinger operator on a lattice in the gap of the essential spectrum”, J. Phys.: Conf. Ser., 2070:1 (2021), 012017
O. O. Pokutnyi, “Boundary-Value Problems for the Evolutionary Schrödinger Equation. I”, J Math Sci, 249:4 (2020), 647
Muminov M.I. Ghoshal S.K., “Spectral Attributes of Self-Adjoint Fredholm Operators in Hilbert Space: a Rudimentary Insight”, Complex Anal. Oper. Theory, 13:3 (2019), 1313–1323
Kholmatov Sh.Yu. Muminov Z.I., “Existence of Bound States of N-Body Problem in An Optical Lattice”, J. Phys. A-Math. Theor., 51:26 (2018), 265202
Muminov M.I. Lokman C., “Finiteness of Discrete Spectrum of the Two-Particle Schrodinger Operator on Diamond Lattices”, Nanosyst.-Phys. Chem. Math., 8:3 (2017), 310–316
M. I. Muminov, N. M. Aliev, “Discrete spectrum of a noncompact perturbation of a three-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 182:3 (2015), 381–396
M. I. Muminov, T. H. Rasulov, “Infiniteness of the number of eigenvalues embedded in the essential spectrum of a $2\times2$ operator matrix”, Eurasian Math. J., 5:2 (2014), 60–77
M. I. Muminov, A. M. Hurramov, “Multiplicity of virtual levels at the lower edge of the continuous spectrum of a two-particle Hamiltonian on a lattice”, Theoret. and Math. Phys., 180:3 (2014), 1040–1050
N. M. Aliev, M. E. Muminov, “On the spectrum of the three-particle Hamiltonian on a unidimensional lattice”, Siberian Adv. Math., 25:3 (2015), 155–168
M. I. Muminov, A. M. Hurramov, “Spectral properties of a two-particle Hamiltonian on a lattice”, Theoret. and Math. Phys., 177:3 (2013), 1693–1705
M. É. Muminov, N. M. Aliev, “Spectrum of the three-particle Schrödinger operator on a one-dimensional lattice”, Theoret. and Math. Phys., 171:3 (2012), 754–768
M. I. Muminov, “Formula for the number of eigenvalues of a three-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 164:1 (2010), 869–882

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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