Revista Matemática Iberoamericana


Full-Text PDF (204 KB) | Metadata | Table of Contents | RMI summary
Volume 34, Issue 3, 2018, pp. 1361–1371
DOI: 10.4171/RMI/1026

Published online: 2018-08-27

Dislocations of arbitrary topology in Coulomb eigenfunctions

Alberto Enciso[1], David Hartley[2] and Daniel Peralta-Salas[3]

(1) Consejo Superior de Investigaciones Científicas, Madrid, Spain
(2) Consejo Superior de Investigaciones Científicas, Madrid, Spain
(3) Consejo Superior de Investigaciones Científicas, Madrid, Spain

For any finite link $L$ in $\mathbb R^3$ we prove the existence of a complex-valued eigenfunction of the Coulomb Hamiltonian such that its nodal set contains a union of connected components diffeomorphic to $L$. This problem goes back to Berry, who constructed such eigenfunctions in the case where $L$ is the trefoil knot or the Hopf link and asked the question about the general result.

Keywords: Coulomb potential, nodal sets, knots

Enciso Alberto, Hartley David, Peralta-Salas Daniel: Dislocations of arbitrary topology in Coulomb eigenfunctions. Rev. Mat. Iberoamericana 34 (2018), 1361-1371. doi: 10.4171/RMI/1026