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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 158, Number 2, Pages 263–276
DOI: https://doi.org/10.4213/tmf6313 (Mi tmf6313) 		 
This article is cited in 6 scientific papers (total in 6 papers)

The number of eigenvalues of the two-particle discrete Schrödinger operator

S. N. Lakaeva, A. M. Khalkhuzhaevb

a A. Navoi Samarkand State University
b Uzbekistan Academy of Sciences, Samarkand Branch
Full-text PDF (441 kB) Citations (6)
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DOI: https://doi.org/10.4213/tmf6313
Abstract: We consider the two-particle discrete Schrödinger operator associated with the Hamiltonian of a system of two particles (fermions) interacting only at the nearest neighbor sites. We find the number and the location of the eigenvalues of this operator depending on the particle interaction energy, the system quasimomentum, and the dimension of the lattice $\mathbb Z^\nu$, $\nu\ge1$.
Keywords: Hamiltonian, two-particle discrete Schrödinger operator, quasimomentum, essential spectrum, virtual level, eigenvalue, Fredholm determinant.
Received: 18.03.2008
Revised: 06.05.2008
English version:
Theoretical and Mathematical Physics, 2009, Volume 158, Issue 2, Pages 221–232
DOI: https://doi.org/10.1007/s11232-009-0018-2
Bibliographic databases:
Language: Russian
Citation: S. N. Lakaev, A. M. Khalkhuzhaev, “The number of eigenvalues of the two-particle discrete Schrödinger operator”, TMF, 158:2 (2009), 263–276; Theoret. and Math. Phys., 158:2 (2009), 221–232
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v158/i2/p263
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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