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arXiv · 1901.01532

Twisted Localized Solutions of the Dirac Equation: Hopfion-like States of Relativistic Electrons

Iwo Bialynicki-Birula·Zofia Bialynicka-Birula
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Abstract

All known solutions of the Dirac equation describing states of electrons endowed with angular momentum are very far from our notion of the electron as a spinning charged bullet because they are not localized in the direction of propagation. We present here analytic exact solutions, eigenstates of the total angular momentum component $M_z$, that come very close to this notion. These new solutions of the Dirac equation have also intricate topological properties similar to the hopfion solutions of the Maxwell equations.

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Iwo Bialynicki-Birula, Zofia Bialynicka-Birula. 2019-06-22. Twisted Localized Solutions of the Dirac Equation: Hopfion-like States of Relativistic Electrons. https://doi.org/10.1103/physreva.100.012108

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