Threshold of discrete Schrödinger operators with delta potentials on $n$-dimensional lattice

Abstract

Eigenvalue behaviors of Schrödinger operator defined on $n$-dimensional lattice with $n+1$ delta potentials is studied. It can be shown that lower threshold eigenvalue and lower threshold resonance are appeared for $n\ge 2$, and lower super-threshold resonance appeared for $n=1$.

30 pages, 6 figures, 4 tables

References in corpus (1)

• The Threshold effects for the two-particle Hamiltonians on lattices