Zh. I. Abdullaev, “Bound states of a system of two fermions on a one-dimensional lattice”, TMF, 147:1 (2006), 47–57; Theoret. and Math. Phys., 147:1 (2006), 486

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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 147, Number 1, Pages 47–57
DOI: https://doi.org/10.4213/tmf2021 (Mi tmf2021)

This article is cited in 9 scientific papers (total in 9 papers)

Bound states of a system of two fermions on a one-dimensional lattice

Zh. I. Abdullaev

A. Navoi Samarkand State University

Full-text PDF (191 kB) Citations (9)

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DOI: https://doi.org/10.4213/tmf2021

Abstract: We consider the Hamiltonian of a system of two fermions on a one-dimensional integer lattice. We prove that the number of bound states $N(k)$ is a nondecreasing function of the total quasimomentum of the system $k\in[0,\pi]$. We describe the set of discontinuity points of $N(k)$ and evaluate the jump $N(k+0)-N(k)$ at the discontinuity points. We establish that the bound-state energy $z_n(k)$ increases as the total quasimomentum $k\in[0,\pi]$ increases.

Keywords: Hamiltonian, bound state, total quasimomentum, Schrödinger operator, eigenvalue, resonance, Birman–Schwinger principle.

Received: 06.06.2005

English version:
Theoretical and Mathematical Physics, 2006, Volume 147, Issue 1, Pages 486–495
DOI: https://doi.org/10.1007/s11232-006-0055-z

Bibliographic databases:

Language: Russian

Citation: Zh. I. Abdullaev, “Bound states of a system of two fermions on a one-dimensional lattice”, TMF, 147:1 (2006), 47–57; Theoret. and Math. Phys., 147:1 (2006), 486–495

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https://doi.org/10.4213/tmf2021

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This publication is cited in the following 9 articles:

J. I. Abdullaev, Sh. H. Ergashova, “Eigenvalues of the Schrödinger Operator Corresponding to a System of Three Fermions on a One Dimensional Lattice”, Lobachevskii J Math, 45:8 (2024), 3821
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. Toshturdiev, “Invariant Subspaces of the Shrödinger Operator with a Finite Support Potential”, Lobachevskii J Math, 43:3 (2022), 728
Abdullaev I J., Khalkhuzhaev A.M., Usmonov L.S., “Monotonicity of the Eigenvalues of the Two-Particle Schrodinger Operatoron a Lattice”, Nanosyst.-Phys. Chem. Math., 12:6 (2021), 657–663
J.I. Abdullaev, Sh.H. Ergashova, Y.S. Shotemirov, “Bound states of a system of two bosons with a spherically potential on a lattice”, J. Phys.: Conf. Ser., 2070:1 (2021), 012023
Janikul Abdullaev, A. M. Toshturdiev, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2365, INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020, 2021, 050008
Zh. I. Abdullaev, K. D. Kuliev, “Bound states of a two-boson system on a two-dimensional lattice”, Theoret. and Math. Phys., 186:2 (2016), 231–250
Abdullayev J., Mamirov B., “Bound states of the system of two fermions on the three-dimensional lattice”, Algebra, Analysis and Quantum Probability, Journal of Physics Conference Series, 697, eds. Ayupov S., Chilin V., Ganikhodjaev N., Mukhamedov F., Rakhimov I., IOP Publishing Ltd, 2016, 012022
Zh. I. Abdullaev, I. A. Ikromov, “Finiteness of the number of eigenvalues of the two-particle Schrödinger operator on a lattice”, Theoret. and Math. Phys., 152:3 (2007), 1299–1312

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

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