On the conditions for the classicality of a quantum particle

TL;DR

This paper investigates conditions where quantum particles can be described classically, identifying specific media that nullify quantum corrections and analyzing wave functions in 1D and 3D cases without assuming small Planck constant.

Contribution

It demonstrates that quantum corrections vanish in certain media, derives the indices of refraction, and characterizes stationary states with classical momenta in 1D and 3D scenarios.

Findings

Quantum corrections sum to zero in specific media.

Wave functions resemble classical particles with zero binding energy.

Stationary states exhibit resonance widths of about two de Broglie wavelengths.

Abstract

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, the wave function is similar to that of the test particle with zero binding energy in a singular attractive potential, which admits "fall" to the center. 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 has the resonance of width about two de Broglie wavelengths.