One dimensional discrete Schr\"odinger operators with resonant embedded eigenvalues
Wencai Liu, Kang Lyu
TL;DR
This paper introduces a novel method for constructing one-dimensional discrete Schrödinger operators with any desired set of embedded eigenvalues by using a new family of functions.
Contribution
It presents a new approach to generate Schrödinger operators with arbitrary embedded eigenvalues, expanding the possibilities for spectral analysis.
Findings
Able to construct operators with prescribed embedded eigenvalues
New family of functions enables flexible spectral design
Advances understanding of embedded eigenvalues in discrete operators
Abstract
In this paper, we introduce a new family of functions to construct Schr\"odinger operators with embedded eigenvalues. This particularly allows us to construct discrete Schr\"odinger operators with arbitrary prescribed sets of eigenvalues.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Mathematical Analysis and Transform Methods · advanced mathematical theories