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We prove that, given any finite link L in R^3, there is a high energycomplex-valued eigenfunction of the harmonic oscillator such that its nodal setcontains a union of connected components diffeomorphic to L. This solves aproblem of Berry on the existence of knotted zeros in bound states of a quantumsystem.

A problem of Berry and knotted zeros in the eigenfunctions of the harmonic oscillator