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

Alberto Enciso, David Hartley, Daniel Peralta-Salas

Published 2015-03-17Version 1

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.