1605.00196v2.pd.pdf (222.73 kB)
0/0

Embedded eigenvalues and Neumann-Wigner potentials for relativistic Schrodinger operators

Download (222.73 kB)
online resource
posted on 07.06.2016 by Jozsef Lorinczi, Itaru Sasaki
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.

History

School

  • Science

Department

  • Mathematical Sciences

Citation

LORINCZI, J. and SASAKI, I., 2015. Embedded eigenvalues and Neumann-Wigner potentials for relativistic Schrodinger operators. arXiv:1605.00196

Publisher

arXiv

Version

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

2015

Notes

Version 2. This is a ArXiv pre-print. It is also available online at: https://arxiv.org/abs/1605.00196v2

Other identifier

arXiv:1605.00196

Language

en

Exports

Logo branding

Keyword(s)

Exports