ABOUT NUMBER AND LOCATION OF EIGENVALUES OF THE DISCRETE SCHRÖDINGER OPERATOR
Keywords:
discrete Schrödinger operator, eigenvalue, essential spectrum.Abstract
We study spectral properties of the discrete Schrödinger operators associated to a system of two identical particles with an indefinite sign interaction potential with energy on nearest neighboring sites and energy on the next nearest neighboring sites on the one-dimensional lattice . We obtain the exact conditions on the parameters for the operator to have zero, one or two eigenvalues outside the essential spectrum.
References
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M.Klaus: On the bound state of Schrödinger operators in one dimension; Annals of Physics 97(1976), 279-288
R.Blankenbecker, M.N.Goldberger and B.Simon: The bound states of a weakly coupled long-range one-dimensional quantum Hamiltonians, Annals of Physics 108(1977), 69-78.
