Deflection of Electrons by a Magnetic Field on the Wave Mechanics

Abstract

The wave equation for a stream of electrons passing through a uniform magnetic field is solved and the characteristic functions discussed. The motion at right angles to the field is found to be completely quantized.The current density is investigated, and the mean square and mean fourth power radii of curvature found for each quantum state. The mean square radius of curvature is found to be the same for all quantum states of the same energy and identical with that predicted by the classical theory.The mean radius of curvature is determined by interpolation and is found to be less than that predicted by the classical theory. Therefore values of $\frac{e}{\ensuremath{\mu}}$ calculated by means of the classical formula from measured values of the mean radius of curvature should be too large. The error is estimated and found to be of the same general magnitude as the discrepancy between the results of deflection experiments and those of spectroscopic measurements.