## 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

### Keywords:

Coulomb potential; nodal sets; knots
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