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

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 .

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Bibliographic Details
Published in:Theoretical and mathematical physics 2009-03, Vol.158 (3), p.360-376
Main Authors: Lakaev, S. N., Bozorov, I. N.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Description
Summary: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 .
ISSN:0040-5779
1573-9333
DOI:10.1007/s11232-009-0030-6