In 2001, Michael Berry published the paper ”Knotted Zeros in the Quantum States of Hydrogen” in Foundationsof Physics. In this paper we show how to place Berry’s discovery in the context of general knot theory and inthe context of our formulations for quantum knots. Berry gave a time independent wave function for hydrogen,as a map from three space R~3 to the complex plane and such that the inverse image of 0 in the complex planecontains a knotted curve in R~3. We show that for knots in R3 this is a generic situation in that every smoothknot K in R~3 has a smooth classifying map f : R~3 −→ C (the complex plane) such that f~(−1)(0) = K. This leavesopen the question of characterizing just when such f are wave-functions for quantum systems. One can comparethis result with the work of Mark Dennis and his collaborators and with the work of Lee Rudolph. Our approachprovides great generality to the structure of knotted zeros of a wavefunction and opens up many new avenuesfor research in the relationships of quantum theory and knot theory. We show how this classifying constructioncan be related our previous work on two dimensional and three dimensional mosaic and lattice quantum knots.
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