Abstract
A theory of twisted (and other structured) paraxial electrons in a uniform magnetic field is developed. The obtained general quantum-mechanical solution of the relativistic paraxial equation contains the commonly accepted result as a specific case of unstructured electron waves. In the weak-field limit, our solution (unlike the existing theory) is consistent with the well-known equation for free twisted electron beams. The observable effect of a different behavior of relativistic Laguerre-Gauss beams with opposite directions of the orbital angular momentum penetrating from the free space into a magnetic field is predicted. Distinguishing features of the quantization of the velocity and the effective mass of structured electrons in the uniform magnetic field are analyzed.
Highlights
The discovery of twisted electron states with a nonzero intrinsic orbital angular momentum (OAM) [2] has confirmed their theoretical prediction [1] and has created new applications of electron beams
The present study describes structured electron states which are not plane waves along the magnetic field direction
The observable effect of a different behavior of relativistic Laguerre-Gauss beams with opposite directions of the orbital angular momentum penetrating from the free space into a magnetic field is predicted
Summary
The discovery of twisted (vortex) electron states with a nonzero intrinsic orbital angular momentum (OAM) [2] has confirmed their theoretical prediction [1] and has created new applications of electron beams. The twisted states of free photons and electrons are defined by the paraxial wave equation [3, 26, 27]: Advanced results obtained in optics allow us to rigorously derive a general formula for the paraxial wave function of a relativistic twisted Dirac particle in a uniform magnetic field.
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