Classical path from quantum motion for a particle in a transparent box

Trajetória clássica a partir do movimento quântico para uma partícula em uma caixa transparente

Abstract

We consider the problem of a free particle inside a one-dimensional box with transparent walls (or equivalently, along a circle with a constant speed) and discuss the classical and quantum descriptions of the problem. After calculating the mean value of the position operator in a time-dependent normalized complex general state and the Fourier series of the function position, we explicitly prove that these two quantities are in accordance by (essentially) imposing the approximation of high principal quantum numbers on the mean value. The presentation is accessible to advanced undergraduate students with a knowledge of the basic ideas of quantum mechanics.

correspondence principle; classical limit; Ehrenfest theorem