Fejer average and the short term behaviors of a wave packet in infinite square well

摘要

The first two period behaviors of a quantum wave packet in an infinite squarewell potential is studied. First, the short term behavior of expectation valueof a quantity on an equally weighted wave packet (EWWP) is in classical limitproved to reproduce the Fej'{e}r average of the Fourier series decomposition ofthe corresponding classical quantity. Second, in order to best mimic theclassical behavior, a nice relation between number $N$ of stationary states inthe EWWP with the average quantum number $n$ as $N\thickapprox \sqrt{n}$ isrevealed. Third, since the Fej\'{e}r average can only approximate the classicalquantity, it carries an uncertainty which in large quantum number case isalmost the same as the quantum uncertainty.