R. G. Novikov, I. A. Taimanov, S. P. Tsarev, “Two-Dimensional von Neumann–Wigner Potentials with a Multiple Positive Eigenvalue”, Funktsional. Anal. i Prilozhen., 2014, Volume 48, Issue 4,Pages <nobr>74

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Brief communications

Two-Dimensional von Neumann–Wigner Potentials with a Multiple Positive Eigenvalue

R. G. Novikov^a, I. A. Taimanov^bc, S. P. Tsarev^d

^a École Polytechnique, Centre de Mathématiques Appliquées
^b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
^c Novosibirsk State University
^d Institute of Space and Information Technologies, Siberian Federal University

Abstract: By the Moutard transformation method we construct two-dimensional Schrödinger operators with real smooth potentials decaying at infinity and having a multiple positive eigenvalue. These potentials are rational functions of spatial variables and their sines and cosines.

Keywords: two-dimensional Schrödinger operator, Moutard transformation, positive eigenvalues.

UDC: 517.95+517.984.5

Received: 02.08.2013

DOI: 10.4213/faa3157