Helical beams of electrons in a magnetic field: New analytic solutions of the Schrödinger and Dirac equations

2023/03/26 by Iwo Białynicki‐Birula, Bialynicki-Birula, Iwo, Zofia Białynicka-Birula +1 · 1 citation
Engineering · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Experimental and Theoretical Physics Studies #FOS: Physical sciences #Mathematical Physics (math-ph) #Particle Accelerators and Free-Electron Lasers #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.2303.14797

openalex publication_date 2023/03/26 · openalex created_date 2023/03/31 · openalex updated_date 2026/07/28

Abstract

We derive new solutions of the Schrödinger, Klein-Gordon and Dirac equations which describe the motion of particles in a uniform magnetic field. In contrast to the well known stationary solutions, our solutions exhibit the behavior of quantum particles which very closely resembles classical helical trajectories. These solutions also serve as an illustration of the meaning of the Ehrenfest theorem in relativistic quantum mechanics.

Cited by

• An amended Ehrenfest theorem for the Gross-Pitaevskii equation in one- and two-dimensional potential boxes

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