Monotonicity of the eigenvalues of the two-particle Schrödinger operatoron a lattice

Abdullaev, J. I.; Khalkhuzhaev, A. M.; Usmonov, L.S.

doi:10.17586/2220-8054-2021-12-6-657-663

Cited by 4 publications

(1 citation statement)

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“…In [19], the authors considered the two-particle Schrödinger operator H(k), (k ∈ T 3 ≡ (−π, π] 3 is the total quasimomentum of a system of two particles) corresponding to the Hamiltonian of the two-particle system on the threedimensional lattice Z 3 . It was proved that the number N (k) ≡ N (k (1) , k (2) , k (3) ) of eigenvalues below the essential spectrum of the operator H(k) is a nondecreasing function in each k (i) ∈ [0, π], i = 1, 2, 3.…”

Section: Introductionmentioning

confidence: 99%

Conditions for the existence of bound states of a two-particle Hamiltonian on a three-dimensional lattice

Muminov¹,

Khurramov²,

Bozorov³

2022

Nanosystems: Phys. Chem. Math.

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The Hamiltonian h of the system of two quantum particles moving on a 3-dimensional lattice interacting via some attractive potential is considered. Conditions for the existence of eigenvalues of the two-particle Schr ödinger operator h µ (k), k ∈ T 3 , µ ∈ R, associated to the Hamiltonian h, are studied depending on the energy of the particle interaction µ ∈ R and total quasi-momentum k ∈ T 3 (T 3 -three-dimensional torus). KEYWORDS two-particle Hamiltonian, invariant subspace, unitary equivalent operator, virtual level, multiplicity of virtual level, eigenvalue.

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Section: Introductionmentioning

confidence: 99%