# Embedded Eigenvalues and Neumann-Wigner Potentials for Relativistic Schrodinger Operators

@article{Lrinczi2016EmbeddedEA, title={Embedded Eigenvalues and Neumann-Wigner Potentials for Relativistic Schrodinger Operators}, author={J{\'o}zsef Lőrinczi and Itaru Sasaki}, journal={arXiv: Mathematical Physics}, year={2016} }

The existence of potentials for relativistic Schrodinger operators allowing eigenvalues embedded in the essential spectrum is a long-standing open problem. We construct Neumann-Wigner type potentials for the massive relativistic Schrodinger operator in one and three dimensions for which an embedded eigenvalue exists. We show that in the non-relativistic limit these potentials converge to the classical Neumann-Wigner and Moses-Tuan potentials, respectively. For the massless operator in one…

## 8 Citations

On Schrödinger and Dirac Operators with an Oscillating Potential

- Physics, Mathematics
- 2019

We review some results on the spectral theory of Schr{o}dinger and Dirac operators. We focus on two aspects: the existence of embbedded eigen-values in the essential spectrum and the limiting…

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We consider non-local Schrödinger operators with kinetic terms given by several different types of functions of the Laplacian and potentials decaying to zero at infinity, and derive conditions ruling…

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- 2020

The purpose of this paper is to give a systematic description of potentials decaying to zero at infinity, which generate eigenvalues at the edge of the absolutely continuous spectrum when combined…

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- Mathematics, PhysicsCommunications in Mathematical Physics
- 2019

We consider solutions of the eigenvalue equation at zero energy for a class of non-local Schrödinger operators with potentials decreasing to zero at infinity. Using a path integral approach, we…

Bulk behaviour of ground states for relativistic Schr\"odinger operators with compactly supported potentials

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- 2021

We show a probabilistic representation of the ground state of a massive or massless Schrödinger operator with a potential well which leads to precise two-sided approximations inside the well in terms…

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- Mathematics, Physics
- 2021

Abstract. We consider half-line Dirac operators with operator data of Wigner-von Neumann type. If the data is a finite linear combination of Wigner-von Neumann functions, we show absence of singular…

Maximum Principles and Aleksandrov-Bakelman-Pucci Type Estimates for NonLocal Schrödinger Equations with Exterior Conditions

- Mathematics, Computer ScienceSIAM J. Math. Anal.
- 2019

This work considers Dirichlet exterior value problems related to a class of non-local Schr\"odinger operators, whose kinetic terms are given in terms of Bernstein functions of the Laplacian, and proves a refined maximum principle in the sense of Berestycki-Nirenberg-Varadhan and a converse.

Embedded eigenvalues of generalized Schrödinger operators

- Physics, Mathematics
- 2017

We provide examples of operators $T(D)+V$ with decaying potentials that have embedded eigenvalues. The decay of the potential depends on the curvature of the Fermi surfaces of constant kinetic energy…

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