Threshold of discrete Schr\"odinger operators with delta potentials on $n$-dimensional lattice

Fumio Hiroshima; Zahriddin Muminov; Utkir Kuljanov

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arXiv · 1804.05339

Threshold of discrete Schr\"odinger operators with delta potentials on $n$-dimensional lattice

Fumio Hiroshima·Zahriddin Muminov·Utkir Kuljanov

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Abstract

Eigenvalue behaviors of Schr\"odinger 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 $n\geq 2$, and lower super-threshold resonance appeared for $n=1$.

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Fumio Hiroshima, Zahriddin Muminov, Utkir Kuljanov. 2018-04-15. Threshold of discrete Schr\"odinger operators with delta potentials on $n$-dimensional lattice. https://arxiv.org/abs/1804.05339

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