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This article is cited in 15 scientific papers (total in 15 papers)
The infiniteness of the number of eigenvalues in the gap in the essential spectrum for the three-particle Schrödinger operator on a lattice
M. I. Muminov A. Navoi Samarkand State University
Abstract:
We consider a system of three arbitrary quantum particles on a three-dimensional lattice that interact via attractive pair contact potentials. We find a condition for a gap to appear in the essential spectrum and prove that there are infinitely many eigenvalues of the Hamiltonian of the corresponding three-particle system in this gap.
Keywords:
three-particle system on a lattice, Schrödinger operator, essential spectrum, discrete spectrum, compact operator.
Received: 14.02.2008 Revised: 22.08.2008
Citation:
M. I. Muminov, “The infiniteness of the number of eigenvalues in the gap in the essential spectrum for the three-particle Schrödinger operator on a lattice”, TMF, 159:2 (2009), 299–317; Theoret. and Math. Phys., 159:2 (2009), 667–683
Linking options:
https://www.mathnet.ru/eng/tmf6350https://doi.org/10.4213/tmf6350 https://www.mathnet.ru/eng/tmf/v159/i2/p299
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Abstract page: | 572 | Full-text PDF : | 241 | References: | 87 | First page: | 7 |
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