We argue that it is nonstationary Laguerre-Gaussian (NSLG) states rather than the Landau ones that appropriately describe electrons with orbital angular momentum both in their dynamics at the boundary between a solenoid and vacuum and inside the magnetic field. It is shown that the root mean square (rms) radius of the NSLG state oscillates in time and its period-averaged value can significantly exceed the rms radius of the stationary Landau state. We propose several experimental scenarios to probe this unconventional quantum dynamics in the magnetic fields typical for electron microscopes and particle accelerators.

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• Beam dynamics
• Electron beams & optics
• Optical vortices
• Quantum state engineering
• Electrons
• Linear accelerators
• Angular momentum
• Particle properties
• Particle beams
• Schroedinger equation