Zh. I. Abdullaev, I. A. Ikromov, “Finiteness of the number of eigenvalues of the two-particle Schrödinger operator on a lattice”, TMF, 152:3 (2007), 502–517; Theoret. and Math. Phys., 152:3 (2007), 1299

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Teoreticheskaya i Matematicheskaya Fizika, 2007, Volume 152, Number 3, Pages 502–517
DOI: https://doi.org/10.4213/tmf6106 (Mi tmf6106)

This article is cited in 12 scientific papers (total in 12 papers)

Finiteness of the number of eigenvalues of the two-particle Schrödinger operator on a lattice

Zh. I. Abdullaev, I. A. Ikromov

A. Navoi Samarkand State University

Full-text PDF (476 kB) Citations (12)

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DOI: https://doi.org/10.4213/tmf6106

Abstract: We consider the two-particle Schrödinger operator

H (k)

$H(k)$ on the

ν

$\nu$ -dimensional lattice

$\mathbb{Z}^{\nu}$ and prove that the number of negative eigenvalues of

$H(k)$ is finite for a wide class of potentials

$\hat{v}$ .

Keywords: Hamiltonian, Schrödinger operator, discrete spectrum, Birman–Schwinger principle.

Received: 19.06.2006
Revised: 02.12.2006

English version:
Theoretical and Mathematical Physics, 2007, Volume 152, Issue 3, Pages 1299–1312
DOI: https://doi.org/10.1007/s11232-007-0114-0

Bibliographic databases:

Language: Russian

Citation: Zh. I. Abdullaev, I. A. Ikromov, “Finiteness of the number of eigenvalues of the two-particle Schrödinger operator on a lattice”, TMF, 152:3 (2007), 502–517; Theoret. and Math. Phys., 152:3 (2007), 1299–1312

Citation in format AMSBIB

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Linking options:

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https://doi.org/10.4213/tmf6106

https://www.mathnet.ru/eng/tmf/v152/i3/p502

This publication is cited in the following 12 articles:

Janikul Abdullaev, Ahmad Khalkhuzhaev, Khabibullo Makhmudov, “DISCRETE SPECTRUM ASYMPTOTICS FOR THE TWO-PARTICLE SCHRÖDINGER OPERATOR ON A LATTICE”, J Math Sci, 2024
Zh. I. Abdullaev, A. M. Khalkhuzhaev, I. S. Shotemirov, “O beskonechnosti chisla sobstvennykh znachenii dvukhchastichnogo operatora Shredingera na reshetke”, Izv. vuzov. Matem., 2024, no. 12, 3–11
J. I. Abdullaev, A. M. Khalkhuzhaev, Kh. Sh. Makhmudov, “The Infiniteness of the Number of Eigenvalues of the Schrödinger Operator of a System of Two Particles on a Lattice”, Lobachevskii J Math, 45:10 (2024), 4828
J. I. Abdullaev, A. M. Khalkhuzhaev, Yu. S. Shotemirov, “On the Infinite Number of Eigenvalues of the Two-Particle Schrödinger Operator on a Lattice”, Russ Math., 68:12 (2024), 25
Zh. I. Abdullaev, A. M. Khalkhuzhaev, T. Kh. Rasulov, “Invariantnye podprostranstva i sobstvennye znacheniya trekhchastichnogo diskretnogo operatora Shredingera”, Izv. vuzov. Matem., 2023, no. 9, 3–19
J. I. Abdullaev, A. M. Khalkhuzhaev, T. H. Rasulov, “Invariant Subspaces and Eigenvalues of the Three-Particle Discrete Schrödinger Operators”, Russ Math., 67:9 (2023), 1
J. I. Abdullaev, A. M. Toshturdiev, “Invariant Subspaces of the Shrödinger Operator with a Finite Support Potential”, Lobachevskii J Math, 43:3 (2022), 728
Muminov I M., Ghoshal S.K., “Spectral Features of Two-Particle Schrodinger Operator on D-Dimensiional Lattice”, Complex Anal. Oper. Theory, 14:1 (2020), 11
Ibrogimov O.O., “Spectral Analysis of the Spin-Boson Hamiltonian With Two Bosons For Arbitrary Coupling and Bounded Dispersion Relation”, Rev. Math. Phys., 32:6 (2020), 2050015
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
Bach V., de Siqueira Pedra W., Lakaev S.N., “Bounds on the Discrete Spectrum of Lattice Schrodinger Operators”, J. Math. Phys., 59:2 (2018), 022109
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

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

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