On eigenvalues and virtual levels of a two-particle Hamiltonian on a d-dimensional lattice
M. I. MuminovV. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, UzbekistanA.M. KhurramovSamarkand State University, Samarkand, UzbekistanI. N. BozorovSamarkand State University, Samarkand, Uzbekistan
Ochiq kirishOlmos
ABI
Annotatsiya
The two-particle Schr dinger operator h (k), k T d (where > 0, T d is a d-dimensional torus), associated to the Hamiltonian h of the system of two quantum particles moving on a d-dimensional lattice, is considered as a perturbation of free Hamiltonian h 0 (k) by the certain 3 d rank potential operator v. The existence conditions of eigenvalues and virtual levels of h (k), are investigated in detail with respect to the particle interaction and total quasi-momentum k T d .
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