EXPANSION OF EIGENVALUES OF SCHRÖDINGER-TYPE OPERATORS ON LATTICES
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Abstract
We study the discrete spectrum of a wide class of discrete Schrödinger-type operators on the two-dimensional lattice where is a Laurent-Toeplitz-type convolution operator, is a finite rank potential and is the coupling constant.
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Sergio Albeverio, S. Lakaev, Z. Muminov: Schrodinger Operators on Lattices. The Efimov Effect and¨ Discrete Spectrum Asymptotics. Ann. Henri Poincar. 5 (2004).
A.T.Boltaev, F.M.Almuratov: The Existence and Asymptotics of Eigenvalues of Schrodinger Operator on Two Dimensional Lattices. Lobachevskii J. Math. 43:12, 3460–3470 (2022)
M. Klaus: On the bound states of Schrodinger operators in one dimension. Ann. Phys.¨ 108 (1977), 288-300.
M. Klaus, B. Simon: Coupling constant thresholds in nonrelativistic Quantum Mechanics. I. Short-range two body case. Ann. Phys. 130 (1980), 251–281.
Sh. Kholmatov, S. Lakaev And F. Almuratov: On the spectrum of Schrodinger-type operators on two dimensional lattices. J. Math. Anal. Appl. 126363 (2022).
Sh. Kholmatov And M. Pardabaev: On spectrum of the discrete bilaplacian with zero-range perturbation. Lobachevskii J. Math. 42, 1286–1293 (2021).
S.N. Lakaev, A.T. Boltaev And F.M. Almuratov: On The discrete spectra of Schrodinger-type operators on one dimensional lattices, Lobachevskii J. Math. 43:3, 1523—1536 (2022).
M. Reed, B. Simon: Modern Methods of Mathematical Physics. IV: Analysis of Operators. Academic Press, New York, 1978.
B. Simon: The bound state of weakly coupled Schrodinger operators in one and two dimensions. Ann. Phys. 97 (1976), 279–288.
F.Almuratov: Ikki oʻlchamli qoʻzgʻalishli model operatorining diskret sреktri Информатика и инженерные технологии 1 (2), 235-238
M Pardabaev, F Almuratov: On the Spectrum of the Discrete Bilaplacian with Rank-One Perturbation, Geometry, Integrability and Quantization, Papers and Lecture Series 26, 39-52