The number of bound states of a one-particle Hamiltonian on a three-dimensional lattice期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The number of bound states of a one-particle Hamiltonian on a three-dimensional lattice

Authors:	S N Lakaev I N Bozorov

Institution:	(1) Samarkand State University, Samarkand, Uzbekistan;(2) Samarkand Division, Academy of Sciences of the Republic of Uzbekistan, Samarkand, Uzbekistan

Abstract:	We consider the Hamiltonian $\hat h_{\mu \lambda } ,\mu ,\lambda \geqslant 0$ , 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.

Keywords:	one-particle Hamiltonian continuous spectrum virtual level eigenvalue Birman-Schwinger operator Fredholm determinant
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