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

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.

arXiv commentSubmitted to Phys. Rev. A

References in corpus (7)

• Electromagnetic Force and Momentum
• Electromagnetic Angular Momentum
• Theory and applications of free-electron vortex states
• Relativistic electron wave packets carrying angular momentum
• A diagrammatic treatment of neutrino oscillations
• Heisenberg uncertainty relation for photons
• Quantum numbers and spectra of structured light

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• Comment on "Fractional Angular Momenta, Gouy and Berry Phases in Relativistic Bateman-Hillion-Gaussian Beams of Electrons" [arXiv:1812.04957]