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Composite Coherent States Approximation for One-Dimensional Multi-Phased Wave Functions

Published online by Cambridge University Press:  20 August 2015

Dongsheng Yin  and
Chunxiong Zheng
Dongsheng Yin*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P.R. China
Chunxiong Zheng*
Affiliation:
Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P.R. China
*
Email:dyin@math.tsinghua.edu.cn
Corresponding author.Email:czheng@math.tsinghua.edu.en
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Abstract

The coherent states approximation for one-dimensional multi-phased wave functions is considered in this paper. The wave functions are assumed to oscillate on a characteristic wave length 0(ε) with ε ≪ 1. A parameter recovery algorithm is first developed for single-phased wave function based on a moment asymptotic analysis. This algorithm is then extended to multi-phased wave functions. If cross points or caustics exist, the coherent states approximation algorithm based on the parameter recovery will fail in some local regions. In this case, we resort to the windowed Fourier transform technique, and propose a composite coherent states approximation method. Numerical experiments show that the number of coherent states derived by the proposed method is much less than that by the direct windowed Fourier transform technique.

Keywords

33F0568W25Coherent statehigh frequencywindowed Fourier transform

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 11 , Issue 3 , March 2012 , pp. 951 - 984
Copyright
Copyright © Global Science Press Limited 2012

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