ANALYSIS OF THE NEGATIVE EIGENVALUES OF THE THREE-DIMENSIONAL DISCRETE SCHRÖDINGER OPERATOR
DOI:
https://doi.org/10.55439/yutsftim/567Abstrak
Eigenvalue behaviour of a family of discrete Schrödinger operators H
depending on parameters , R is studied on the three-dimensional lattice 3 Z . The
non-local potential is described by the Kronecker delta function and the shift operator.
The existence of eigenvalues below the essential spectrum and their dependence on the
parameters are explicitely proven. We also show that the essential spectrum absorbes
the threshold eigenvalue and there exists a particular parabola, on whose left intercept
the threshold becomes an embedded eigenvalue and the threshold resonance at its
other points.
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