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Title: Embedded eigenvalues and Neumann-Wigner potentials for relativistic Schrodinger operators
Authors: Lorinczi, Jozsef
Sasaki, Itaru
Issue Date: 2015
Publisher: arXiv
Citation: LORINCZI, J. and SASAKI, I., 2015. Embedded eigenvalues and Neumann-Wigner potentials for relativistic Schrodinger operators. arXiv:1605.00196
Abstract: We 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.
Description: Version 2. This is a ArXiv pre-print. It is also available online at: https://arxiv.org/abs/1605.00196v2
Version: Submitted for publication
URI: https://dspace.lboro.ac.uk/2134/21506
Publisher Link: https://arxiv.org/abs/1605.00196v2
Appears in Collections:Pre-prints (Maths)

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