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

European Mathematical Society 2018 We prove that, given any finite link L in R 3 , 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.