Orbital angular momentum, its torque and magnetic moment calculated for the electrons circulating on the Landau levels of a crystalline solid

Abstract

The angular momentum of electrons circulating in a constant magnetic field has been examined for the case of free electrons and those bound in a crystal lattice. The case of the crystal electrons provides us with a change of the angular momentum in the course of the process of the electron circulation. This temporal dependence can then be associated with the relaxation time of the circulation varying along the electron position on the orbit. The quantum expressions for the angular momentum and the magnetic moment, similar to those calculated for the energies of the Landau levels, have been derived and compared, first, with the experimental data for semiconductors, next with those obtained by Askenazy. For semiconductors the average observed data differ from those calculated from the theory by a factor equal to about two. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of a Magnetic Field on an Atomic Orbital

“…A more thoughtful idea is to attribute the speed change to the modified centripetal force and to assert a fixed radius. Even though there has been considerable interest in the effect of magnetic field on the motion of an electron [4][5][6][7][8], but there has been no direct investigation of the above problem for the general case in which both the speed and the radius are allowed to change. Therefore in the present paper we discuss the effect of an external magnetic field on an atomic orbital electron.…”