For any finite link $L$ in $\mathbb{ R}^3$ we prove the existence of a high-energy complex-valued eigenfunction of the hydrogen atom 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.
Categories: math-ph math.MP math.SP