For any finite link in 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 . This problem goes back to Berry, who constructed such eigenfunctions in the case where is the trefoil knot or the Hopf link and asked the question about the general result.
Cite this article
Alberto Enciso, David Hartley, Daniel Peralta-Salas, Dislocations of arbitrary topology in Coulomb eigenfunctions. Rev. Mat. Iberoam. 34 (2018), no. 3, pp. 1361–1371DOI 10.4171/RMI/1026