A problem of Berry and knotted zeros in the eigenfunctions of the harmonic oscillator
Mathematical Physics
2015-03-18 v1 math.MP
Spectral Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1503.05101,
title = {A problem of Berry and knotted zeros in the eigenfunctions of the harmonic oscillator},
author = {Alberto Enciso and David Hartley and Daniel Peralta-Salas},
journal= {arXiv preprint arXiv:1503.05101},
year = {2015}
}
Comments
12 pages