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Full-Text Articles in Physical Sciences and Mathematics
On Negative Eigenvalues Of The Discrete Schrödinger Operator With Non-Local Potential, Zahriddin Muminov, Shukhrat Lakaev
On Negative Eigenvalues Of The Discrete Schrödinger Operator With Non-Local Potential, Zahriddin Muminov, Shukhrat Lakaev
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
On the d-dimensional lattice 𝕋d, d= 1, 2 the discrete Schrödinger operator Hλµ with non-local potential constructed via the Dirac delta function and shift operator is considered. The dependency of negative eigenvalues of the operator on the parameters is explicitly derived.
On Negative Eigenvalues Of The Discrete Schrödinger Operator With Non-Local Potential, Zahriddin Muminov, Shukhrat Lakaev
On Negative Eigenvalues Of The Discrete Schrödinger Operator With Non-Local Potential, Zahriddin Muminov, Shukhrat Lakaev
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
On the d-dimensional lattice 𝕋d, d= 1, 2 the discrete Schrödinger operator Hλµ with non-local potential constructed via the Dirac delta function and shift operator is considered. The dependency of negative eigenvalues of the operator on the parameters is explicitly derived.
On The Number Of The Discrete Spectrum Of Two-Particle Discrete Schröodinger Operators, Zahriddin Muminov, Utkir Kuljanov, Shukhrat Alladustov
On The Number Of The Discrete Spectrum Of Two-Particle Discrete Schröodinger Operators, Zahriddin Muminov, Utkir Kuljanov, Shukhrat Alladustov
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
We consider a family of discrete Schrö dinger operators hd(k), where k is the two-particle quasi-momentum varying in 𝕋d=(−π,π]d , associated to a system of two-particles on the d - dimensional lattice ℤd, d>1. The CwikelLieb-Rozenblum (CLR)-type estimates are written for hd(k) when the Fermi surface Ek-1(𝔢m(k)) of the associated dispersion relation is a one point set at em(k), the bottom of the essential spectrum. Moreover, when the Fermi surface Ek-1(𝔢m(k)) is of dimension d−1 or d−2, we …