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Dislocations of arbitrary topology in Coulomb eigenfunctions. (English) Zbl 1400.35011

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.

MSC:

35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35J10 Schrödinger operator, Schrödinger equation
35P05 General topics in linear spectral theory for PDEs
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