ON THE NUMBER AND LOCATION OF EIGENVALUES OF THE DISCRETE SCHRÖDINGER OPERATOR ON A LATTICE
Keywords:
eigenvalues, essential spectrum, discrete 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.
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