1605.00196v2.pd.pdf (222.73 kB)
Embedded eigenvalues and Neumann-Wigner potentials for relativistic Schrodinger operators
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posted on 2016-06-07, 11:28 authored by Jozsef Lorinczi, Itaru SasakiWe construct Neumann-Wigner type potentials for the massive relativistic Schrodinger operator in one and three dimensions for which an eigenvalue embedded in the bsolutely continuous spectrum exists. First we consider the relativistic variants of the original example by von Neumann and Wigner, and as a second example we discuss the potential due to Moses and Tuan. We show that in the non-relativistic limit these potentials converge to the classical Neumann-Wigner potentials. For the massless operator in one dimension we construct two families of potentials, different by the parities of the (generalized) eigenfunctions, for which an eigenvalue equal to zero or a 0-resonance exists, dependent on the rate of decay of the corresponding eigenfunctions.
History
School
- Science
Department
- Mathematical Sciences
Citation
LORINCZI, J. and SASAKI, I., 2015. Embedded eigenvalues and Neumann-Wigner potentials for relativistic Schrodinger operators. arXiv:1605.00196Publisher
arXivVersion
- SMUR (Submitted Manuscript Under Review)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2015Notes
Version 2. This is a ArXiv pre-print. It is also available online at: https://arxiv.org/abs/1605.00196v2Publisher version
Other identifier
arXiv:1605.00196Language
- en