Dislocations of arbitrary topology in Coulomb eigenfunctions (Q1989549)

Summary: 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.