Finiteness of the discrete spectrum of the three-particle schrödinger equation on a lattice |
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Authors: | Zh I Abdullaev S N Lakaev |
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Institution: | (1) Samarkand State University, Samarkand, Republic of Uzbekistan |
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Abstract: | Consideration is given to the Hamiltonian of a system of three identical quantum particles on a lattice that interact via pairwise contact attractive potentials. Finiteness of the three-particle bound states is proved for the three-dimensional discrete Schrödinger operator on the condition that the operators describing the two-particle subsystems have no virtual levels. For high dimensions (v ≥ 5), the finiteness of three-particle bound states is also proved in the presence of virtual levels. |
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