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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 9 scientific papers (total in 9 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 (9)
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DOI: https://doi.org/10.4213/tmf6106
Abstract: We consider the two-particle Schrödinger operator $H(k)$ on the $\nu$-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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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:83
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