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