Observation of matter wave beat phenomena in the macrodomain for electrons moving along a magnetic field

Abstract

We report here the observations that exhibit the existence of matter wave phenomena with wavelength in the macrodomain of a few centimeters, for electrons moving along a magnetic field from an electron gun to a collector plate situated behind a grounded grid. These are in accordance with the predictions of a quantumlike theory for charged particles in the classical macrodomain, given by one of the authors [R. K. Varma, Phys. Rev. A 31, 3951 (1985)] with a recent generalization [R. K. Varma, Phys. Rev. E 64, 036608 (2001)]. The beats correspond to two closely spaced "frequencies" in the system, with the beat frequency given, in accordance with the characteristics of a wave phenomena, by the difference between the two frequencies. The beats ride as a modulation over a discrete energy band structure obtained with only one frequency present. The frequency here corresponds to the distance between the electron gun and the detector plate as it characterizes the variation in the energy band structure as the electron energy is swept. The second "frequency" corresponds to the gun-grid distance. These observations of the beats of matter waves in this experiment, with characteristics in accordance with the wave algorithm, then establish unambiguously the existence of macroscopic matter waves for electrons propagating along a magnetic field.