Search

In this paper we introduce an alternative approach to studying the motion of a planar charged particle subject to a static uniform magnetic field. It is well known that an electric charge under a uniform magnetic field has a planar motion if its initial velocity is perpendicular to the magnetic field. Although some constants of motion (CsM), as the energy and the angular momentum, have been widely discussed for this system, others have been neglected. We find that the angular momentum, the generator of the magnetic translations and the magnetic Laplace–Runge–Lenz vector are CsM for this particular system. We show also that these three quantities form an orthogonal basis of vectors. The present work addresses many aspects of the motion of a charged particle in a magnetic field that should be useful for students and tutors of the classical mechanics courses at the senior undergraduate level.

Using the exact two-propagating-modes solutions for electrons in a quasi-2D semiconductor wave guide under sectionally constant magnetic fields and spin-orbit interactions, it is explicitly shown that the Fano-like resonances and antiresonances lead to sudden suppressions and enhancements of the spin-dependent transmission probabilities. Our calculations show that when the magnetic-field-tilting angle θH is increased, the spin-field interaction becomes the most significant mechanism for the spin transitions in magnetic superlattices. Taking advantage of these spin-transport effects, simple and efficient spin-inverter devices are proposed. To better visualize the relative influence of the specific semiconductor properties on the device performance and device characteristics, we consider two magnetic superlattices based on semiconductors having entirely different Lande g-factor: GaAs and InSb. Although slightly more efficient spin-inversion devices are obtained for the GaAs semiconductor, InSb requires lower magnetic fields and its efficiency can be close to 80%.