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Finiteness of the number of eigenvalues of the two-particle Schrödinger operator on a lattice

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Abstract

We consider the two-particle Schrödinger operator H(k) on the ν-dimensional lattice ℤν and prove that the number of negative eigenvalues of H(k) is finite for a wide class of potentials \(\hat v\).

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Authors and Affiliations

  1. Samarkand State University, Samarkand, Uzbekistan

    J. I. Abdullaev & I. A. Ikromov

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  1. J. I. Abdullaev
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  2. I. A. Ikromov
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Correspondence to J. I. Abdullaev.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 502–517, September, 2007.

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Abdullaev, J.I., Ikromov, I.A. Finiteness of the number of eigenvalues of the two-particle Schrödinger operator on a lattice. Theor Math Phys 152, 1299–1312 (2007). https://doi.org/10.1007/s11232-007-0114-0

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  • DOI: https://doi.org/10.1007/s11232-007-0114-0

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