Zh. I. Abdullaev, S. N. Lakaev, “Finiteness of discrete spectrum of three particle Schrödinger operator on the lattice”, TMF, 111:1 (1997), 94–108; Theoret. and Math. Phys., 111:1 (1997), 467

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Teoreticheskaya i Matematicheskaya Fizika, 1997, Volume 111, Number 1, Pages 94–108
DOI: https://doi.org/10.4213/tmf992 (Mi tmf992)

This article is cited in 35 scientific papers (total in 35 papers)

Finiteness of discrete spectrum of three particle Schrödinger operator on the lattice

Zh. I. Abdullaev, S. N. Lakaev

A. Navoi Samarkand State University

Full-text PDF (279 kB) Citations (35)

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DOI: https://doi.org/10.4213/tmf992

Abstract: A Hamiltonian system of three identical quantum particles on a lattice interacting via pairwise contact attracting potentials is discussed. Finiteness of three particle bound states of the three dimensional Schrödinger operator is proved under the condition that operators describing two particle subsystems do not have virtual levels. For high dimensions

(ν \geq 5)

$(\nu\geq5)$ the finiteness of three particle bound states is also proved under the presence of virtual levels.

Received: 07.06.1996

English version:
Theoretical and Mathematical Physics, 1997, Volume 111, Issue 1, Pages 467–479
DOI: https://doi.org/10.1007/BF02634201

Bibliographic databases:

Language: Russian

Citation: Zh. I. Abdullaev, S. N. Lakaev, “Finiteness of discrete spectrum of three particle Schrödinger operator on the lattice”, TMF, 111:1 (1997), 94–108; Theoret. and Math. Phys., 111:1 (1997), 467–479

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf992

https://doi.org/10.4213/tmf992

https://www.mathnet.ru/eng/tmf/v111/i1/p94

This publication is cited in the following 35 articles:

Muminov Z.E., Lakaev Sh.S., Aliev N.M., “On the Essential Spectrum of Three-Particle Discrete Schrodinger Operators With Short-Range Potentials”, Lobachevskii J. Math., 42:6, SI (2021), 1304–1316
S. N. Lakaev, A. T. Boltaev, “Threshold phenomena in the spectrum of the two-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 198:3 (2019), 363–375
M. E. Muminov, E. M. Shermatova, “On finiteness of discrete spectrum of three-particle Schrödinger operator on a lattice”, Russian Math. (Iz. VUZ), 60:1 (2016), 22–29
Rasulov T.H., “on the Finiteness of the Discrete Spectrum of a 3 X 3 Operator Matrix”, Methods Funct. Anal. Topol., 22:1 (2016), 48–61
M. I. Muminov, A. M. Khurramov, “On compact distribution of two-particle Schrödinger operator on a lattice”, Russian Math. (Iz. VUZ), 59:6 (2015), 18–22
T. Kh. Rasulov, R. T. Mukhitdinov, “The finiteness of the discrete spectrum of a model operator associated with a system of three particles on a lattice”, Russian Math. (Iz. VUZ), 58:1 (2014), 52–59
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
Lakaev S., Darus M., Kurbanov Sh., “Puiseux Series Expansion for an Eigenvalue of the Generalized Friedrichs Model with Perturbation of Rank 1”, J. Phys. A-Math. Theor., 46:20 (2013), 205304
Yu. Kh. Eshkabilov, R. R. Kucharov, “Essential and discrete spectra of the three-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 170:3 (2012), 341–353
I. I. Filatova, F. M. Trukhachev, N. I. Chubrik, “Study of the process of dust grain discharging in the afterglow of an RF discharge”, Plasma Phys. Rep., 37:12 (2011), 1042
Rasulov T.H., “Investigations of the Essential Spectrum of a Hamiltonian in Fock Space”, Applied Mathematics & Information Sciences, 4:3 (2010), 395–412
E. Yu. Loktionov, Yu. Yu. Protasov, “A light-erosion method for high-pressure dust-gas-plasma flows generation”, Instrum Exp Tech, 53:4 (2010), 601
Albeverio, S, “THE ESSENTIAL AND DISCRETE SPECTRUM OF A MODEL OPERATOR ASSOCIATED TO A SYSTEM OF THREE IDENTICAL QUANTUM PARTICLES”, Reports on Mathematical Physics, 63:3 (2009), 359
Zh. I. Abdullaev, “Finiteness of discrete spectra for nontrivial values of the full quasi-momentum in the system of three bosons on a lattice”, Russian Math. Surveys, 62:1 (2007), 175–177
T. H. Rasulov, “Discrete spectrum of a model operator in Fock space”, Theoret. and Math. Phys., 152:3 (2007), 1313–1321
Albeverio, S, “On the structure of the essential spectrum for the three-particle Schrodinger operators on lattices”, Mathematische Nachrichten, 280:7 (2007), 699
A. V. Filippov, A. F. Pal', A. N. Starostin, A. S. Ivanov, “Electrostatic interaction between two macroparticles in the Poisson-Boltzmann model”, JETP Letters, 83:12 (2006), 546–552
Albeverio, S, “Schrodinger operators on lattices. The Efimov effect and discrete spectrum asymptotics”, Annales Henri Poincare, 5:4 (2004), 743
Zh. I. Abdullaev, S. N. Lakaev, “Asymptotics of the Discrete Spectrum of the Three-Particle Schrödinger Difference Operator on a Lattice”, Theoret. and Math. Phys., 136:2 (2003), 1096–1109
Albeverio, S, “On the finiteness of the discrete spectrum of four-particle lattice Schrodinger operators”, Reports on Mathematical Physics, 51:1 (2003), 43

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

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