Abstract
Complex superpositions of degenerate hydrogen wavefunctions for the n th energy level can possess zero lines (phase singularities) in the form of knots and links. A recipe is given for constructing any torus knot. The simplest cases are constructed explicitly: the elementary link, requiring n≥6, and the trefoil knot, requiring n≥7. The knots are threaded by multistranded twisted chains of zeros. Some speculations about knots in general complex quantum energy eigenfunctions are presented.
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Berry, M. Knotted Zeros in the Quantum States of Hydrogen. Foundations of Physics 31, 659–667 (2001). https://doi.org/10.1023/A:1017521126923
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DOI: https://doi.org/10.1023/A:1017521126923