On the conditions for the classicality of a quantum particle

V. E. Kuzmichev, V. V. Kuzmichev

Published 2020-07-23Version 1

Conditions under which a quantum particle is described using classical quantities are studied. The one-dimensional (1D) and three-dimensional (3D) problems are considered. It is shown that the sum of the contributions from all quantum corrections (in the WKB sense) strictly vanishes, when a quantum particle interacts with some specific medium. The indices of refraction of such media are found. In this case, the smallness of the Planck constant is not assumed. The momenta of quantum particles in these media and the wave functions of stationary states are determined. It is found that, for the 1D case, there is a localization of the wave in the region of the order of a few de Broglie wavelengths for any finite energy of a quantum particle. For the 3D case with central symmetry, a stationary state, describing a quantum particle with a classical momentum, is defined by the wave function, which takes almost constant values in the region of small values of the index of refraction. The oscillations are damped smoothly with the increase of the index of refraction, so that, the wave packet is formed.