The Fejér average and the mean value of a quantity in a quasiclassical wave packet

Quanhui Liu; Xin Wang; Weihong Qi; Liping Fu; Bambi Hu

doi:10.1063/1.1418245

The Fejér average and the mean value of a quantity in a quasiclassical wave packet

Quanhui Liu^*
, Xin Wang
, Weihong Qi
, Liping Fu
, Bambi Hu

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

7 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	170-181
Number of pages	12
Journal	Journal of Mathematical Physics
Volume	43
Issue number	1
DOIs	https://doi.org/10.1063/1.1418245
Publication status	Published - Jan 2002

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abstract = "The mean value of a quantity in an equally weighted wave packet was recently found in the classical limit to be the Fej{\'e}r 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 Fej{\'e}r 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.",

author = "Quanhui Liu and Xin Wang and Weihong Qi and Liping Fu and Bambi Hu",

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AU - Fu, Liping

AU - Hu, Bambi

N1 - This work is supported in part by National Natural Science Foundation of China through Grant No: 19974010; in part by grants from the Hong Kong Research Grants Council (RGC), and the Hong Kong Baptist University Faculty Research Grant (FRG). Publisher copyright: © 2002 American Institute of Physics.

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N2 - 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.

AB - 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.

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JO - Journal of Mathematical Physics

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The Fejér average and the mean value of a quantity in a quasiclassical wave packet

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