A problem of Berry and knotted zeros in the eigenfunctions of the harmonic oscillator

  • Alberto Enciso

    ICMAT, Madrid, Spain
  • David Hartley

    University of Wollongong, Australia
  • Daniel Peralta-Salas

    ICMAT, Madrid, Spain

Abstract

We prove that, given any finite link in , there is a high-energy complex-valued eigenfunction of the harmonic oscillator such that its nodal set contains a union of connected components diffeomorphic to . This solves a problem of Berry on the existence of knotted zeros in bound states of a quantum system.

Cite this article

Alberto Enciso, David Hartley, Daniel Peralta-Salas, A problem of Berry and knotted zeros in the eigenfunctions of the harmonic oscillator. J. Eur. Math. Soc. 20 (2018), no. 2, pp. 301–314

DOI 10.4171/JEMS/767