Helical beams of electrons in a magnetic field: new analytic solutions of the Schrödinger and Dirac equations. (English) Zbl 1526.81039
Summary: 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.
MSC:
| 81V10 | Electromagnetic interaction; quantum electrodynamics |
| 78A35 | Motion of charged particles |
| 78A30 | Electro- and magnetostatics |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 35A09 | Classical solutions to PDEs |
| 70K42 | Equilibria and periodic trajectories for nonlinear problems in mechanics |
| 81R20 | Covariant wave equations in quantum theory, relativistic quantum mechanics |
Software:
MathematicaReferences:
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