search for
A Bessel Beam Solution for Relativistic Electron Vortices
New Phys.: Sae Mulli 2020; 70: 175~180
Published online February 28, 2020;
© 2020 New Physics: Sae Mulli.

Yeong Deok HAN*

Department of Computer Science, Woosuk University, Jincheon 27841, Korea
Correspondence to:
Received November 4, 2019; Revised December 26, 2019; Accepted December 30, 2019.
cc This is an open-access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
In non-relativistic electron vortex beams, the spin of an electron is treated as a degree of freedom independent from the momentum of the electron. However, for a relativistic electron described by the Dirac equation, its spin is intimately related to its momentum, as is manifested by spin-orbit coupling, helicity conservation, etc. In this paper, we construct a Bessel beam solution by superposing momentum eigen functions, whose spins are parallel to the momentum or at a constant angle with the beam axis. By introducing a Gaussian envelope function for the normalization of the wave functions, we calculate the expectation values for physical quantities such as the spin and magnetic moment. Also, the differences from the results of previous studies are discussed.
PACS numbers: 41.85.-p, 03.65.Pm
Keywords: Relativistic electron vortex beam, Bessel beam, Spin, Magnetic moment

March 2020, 70 (3)
  • Scopus
  • CrossMark