Conditions for the existence of bound states of a two-particle Hamiltonian on a three-dimensional lattice
M. I. MuminovSamarkand State University, Samarkand, 140104, UzbekistanA.M. KhurramovSamarkand State University, Samarkand, 140104, UzbekistanI. N. BozorovSamarkand State University, Samarkand, 140104, Uzbekistan
ABI
Abstract
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 dinger operator h (k), k T 3 , R, associated to the Hamiltonian h, are studied depending on the energy of the particle interaction R and total quasi-momentum k T 3 (T 3 -three-dimensional torus).
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