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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 158, Number 3, Pages 425–443
DOI: https://doi.org/10.4213/tmf6325 (Mi tmf6325) 		 
This article is cited in 23 scientific papers (total in 23 papers)

The number of bound states of a one-particle Hamiltonian on a three-dimensional lattice

S. N. Lakaeva, I. N. Bozorovb

a A. Navoi Samarkand State University
b Uzbekistan Academy of Sciences, Samarkand Branch
Full-text PDF (473 kB) Citations (23)
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DOI: https://doi.org/10.4213/tmf6325
Abstract: We consider the Hamiltonian $\hat h_{\mu\lambda}$, $\mu,\lambda\ge0$, describing the motion of one quantum particle on a three-dimensional lattice in an external field. We investigate the number of eigenvalues and their arrangement depending on the value of the interaction energy for $\mu\ge0$ and $\lambda\ge0$.
Keywords: one-particle Hamiltonian, continuous spectrum, virtual level, eigenvalue, Birman—Schwinger operator, Fredholm determinant.
Received: 15.04.2008
Revised: 23.06.2008
English version:
Theoretical and Mathematical Physics, 2009, Volume 158, Issue 3, Pages 360–376
DOI: https://doi.org/10.1007/s11232-009-0030-6
Bibliographic databases:
Language: Russian
Citation: S. N. Lakaev, I. N. Bozorov, “The number of bound states of a one-particle Hamiltonian on a three-dimensional lattice”, TMF, 158:3 (2009), 425–443; Theoret. and Math. Phys., 158:3 (2009), 360–376
Citation in format AMSBIB
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    • This publication is cited in the following 23 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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