The number of bound states of a one-particle Hamiltonian on a three-dimensional lattice |
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Authors: | S. N. Lakaev I. N. Bozorov |
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Affiliation: | (1) Samarkand State University, Samarkand, Uzbekistan;(2) Samarkand Division, Academy of Sciences of the Republic of Uzbekistan, Samarkand, Uzbekistan |
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Abstract: | We consider the Hamiltonian , describing the motion of one quantum particle on a three-dimensional lattice in an external field. We investigate the number of eigenvalues and their arrangement depending on the value of the interaction energy for μ ≥ 0 and λ ≥ 0. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 425–443, March, 2009. |
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Keywords: | one-particle Hamiltonian continuous spectrum virtual level eigenvalue Birman-Schwinger operator Fredholm determinant |
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