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

Authors

Alberto Enciso, Institute of Mathematical Sciences
David James Hartley, University of WollongongFollow
Daniel Peralta-Salas, Institute of Mathematical Sciences

RIS ID

125543

Publication Details

Enciso, A., Hartley, D. & Peralta-Salas, D. (2018). A problem of Berry and knotted zeros in the eigenfunctions of the harmonic oscillator. Journal of the European Mathematical Society, 20 (2), 301-314.

Abstract

European Mathematical Society 2018 We prove that, given any finite link L in R 3 , 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 L. This solves a problem of Berry on the existence of knotted zeros in bound states of a quantum system.