JournalsjstVol. 3, No. 2pp. 147–169

Schrödinger operators with slowly decaying Wigner–von Neumann type potentials

  • Milivoje Lukic

    Rice University, Houston, USA
Schrödinger operators with slowly decaying Wigner–von Neumann type potentials cover
Download PDF

Abstract

We consider Schr\"odinger operators with potentials satisfying a generalized bounded variation condition at infinity and an LpL^p decay condition. This class of potentials includes slowly decaying Wigner--von~Neumann type potentials sin(ax)/xb\sin(ax)/x^b with b>0b>0. We prove absence of singular continuous spectrum and show that embedded eigenvalues in the continuous spectrum can only take values from an explicit finite set. Conversely, we construct examples where such embedded eigenvalues are present, with exact asymptotics for the corresponding eigensolutions.

Cite this article

Milivoje Lukic, Schrödinger operators with slowly decaying Wigner–von Neumann type potentials. J. Spectr. Theory 3 (2013), no. 2, pp. 147–169

DOI 10.4171/JST/41