# On the embedded eigenvalue of relativistic Schrodinger operator

Itaru Sasaki
(Shinshu University)
Math/Phys Seminar
Wednesday, 6 December, 2017, at 15:15-16:00, in Aud. D1 (1531-113)
Abstract:
The Schrodinger operator do not have positive eigenvalues if the potential
decays fast. But slowly decaying potentials can make a positive
eigenvalue. In 1929, von Neumann and Wigner constructed a concrete
example for which a potential can make a positive energy eigenvalue.
Their constructed potential decays as sin(2x)/|x|.

In this talk we construct von Neumann-Wigner type potentials for the
massive relativistic Schrodinger operators for which an embedded
eigenvalue exists. We also discuss the non-relativistic limit and show
that our constructed potentials converge to the classical  Neumann-
Wigner's potential.
Contact person: Jacob Schach Møller