The mean value of a quantity in an equally weighted wave packet was recently found in the classical limit to be the Fejér average of partial sums of Fourier series expansion of the classical quantity, and the number of stationary states in it is equal to that of partial sums. The incompleteness of the Fejér average in representing a classical quantity enables us to define a classical uncertainty relation which turns out to be the counterpart of the quantum one. In this paper, two typical quantum systems, a harmonic oscillator and a particle in an infinite square well, are used to illustrate the above-mentioned points.

1.
The Physics and Chemistry of Wave Packets, edited by J. A. Yeazell and T. Uzer (Wiley, New York, 2000).
2.
L. D. Landau and E. M. Lifshitz, Quantum Mechanics(non-relativistic theory) (Pergamon, New York, 1987), p. 173.
3.
Q. H.
Liu
,
J. Phys. A
32
,
L57
(
1999
).
4.
D. L.
Arostein
and
C. R.
Stroud
, Jr.
,
Phys. Rev. A
55
,
4526
(
1997
).
5.
J.-P. Kahane and P.-G. Lemarie-Rieusset, Fourier Series and Wavelets (Gordon and Breach, Luxembourg, 1995).
6.
G. H. Hardy and W. W. Rogosinski, Fourier Series, 3rd ed. (Cambridge University Press, Cambridge, 1956).
7.
A. J. Jerri, The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations (Kluwer, London, 1998).
8.
D.
Gottlib
and
C. W.
Shu
,
SIAM Rev.
39
,
644
(
1997
).
9.
L. E.
Ballentine
,
Rev. Mod. Phys.
42
,
358
(
1970
).
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