Classical Limit of Expectation Values in a Wave Packet Involving Few Stationary States

Abstract

Expectation values of physical quantities in a wave packet involving few stationary states in an infinite square well are calculated. Explicit results show that the expectation values in the classical limit go over to the corresponding classical quantity in the form of the arithmetic mean (in mathematical term, the Fejer's average) of the partial Fourier series converging to the classical quantity. The number of the stationary states is that of the partial Fourer series in the Fejer's average. The quantum uncertainty is then demonstrated to have a classical counterpart.