Geodesic
A problem of Berry and knotted zeros in the eigenfunctions of the harmonic oscillator
Journal of the European Mathematical Society, Tome 20 (2018) no. 2, pp. 301-314

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We prove that, given any finite link L in R3, there is a high-energy complex-valued eigenfunction of the harmonic oscillator such that its nodal set contains a union of connected components diffeomorphic to L. This solves a problem of Berry on the existence of knotted zeros in bound states of a quantum system.
DOI : 10.4171/jems/767
Classification : 35-XX
Keywords: Eigenfunctions, harmonic oscillator, nodal sets, knots and links 
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     author = {Alberto Enciso and David Hartley and Daniel Peralta-Salas},
     title = {A problem of {Berry} and knotted zeros in the eigenfunctions of the harmonic oscillator},
     journal = {Journal of the European Mathematical Society},
     pages = {301--314},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2018},
     doi = {10.4171/jems/767},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/767/}
}
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Alberto Enciso; David Hartley; Daniel Peralta-Salas. A problem of Berry and knotted zeros in the eigenfunctions of the harmonic oscillator. Journal of the European Mathematical Society, Tome 20 (2018) no. 2, pp. 301-314. doi: 10.4171/jems/767

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