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2022•Ilmiy axborotnoma/Scientific Journal of Samarkand UniversityOpen access

THE EXICTENCE OF EIGENVALUES AND THE ESSENTIAL SPECTRUM OF THE TWO-PARTICLE DISCRETE SCHRÖDINGER OPERATOR ON LATTICES

S. N. Lakaev, S h I Hamidov, S A b d u v a y i t o

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Abstract

We study a two-particle discrete Schrödinger operator associated with a system of three particles moving on the three-dimensional cubic lattice depending on the interaction magnitude and particles mass ratio . We establish the essential spectrum of the two-particle discrete Schrödinger operator and prove the existence of eigenvalues located below the bottom of the essential spectrum of two-particle discrete Schrödinger operator for all , under the assumption that the bottom of the essential spectrum is a resonance (virtual level) of operator

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We study a two-particle discrete Schrödinger operator associated with a system of three particles moving on the three-dimensional cubic lattice depending on the interaction magnitude and particles mass ratio . We establish the essential spectrum of the two-particle discrete Schrödinger operator and prove the existence of eigenvalues located below the bottom of the essential spectrum of two-particle discrete Schrödinger operator for all , under the assumption that the bottom of the essential spectrum is a resonance (virtual level) of operator

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Available abstract

We study a two-particle discrete Schrödinger operator associated with a system of three particles moving on the three-dimensional cubic lattice depending on the interaction magnitude and particles mass ratio . We establish the essential spectrum of the two-particle discrete Schrödinger operator and prove the existence of eigenvalues located below the bottom of the essential spectrum of two-particle discrete Schrödinger operator for all , under the assumption that the bottom of the essential spectrum is a resonance (virtual level) of operator

Key concepts: Essential spectrum, Discrete spectrum, Eigenvalues and eigenvectors, Operator (biology), Spectrum (functional analysis), Schrödinger's cat, Continuous spectrum, Lattice (music)

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