Volume 11, Issue 3
Composite Coherent States Approximation for One-Dimensional Multi-Phased Wave Functions

Dongsheng Yin & Chunxiong Zheng

Commun. Comput. Phys., 11 (2012), pp. 951-984.

Published online: 2012-11

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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 O(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. 

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@Article{CiCP-11-951, author = {}, title = {Composite Coherent States Approximation for One-Dimensional Multi-Phased Wave Functions}, journal = {Communications in Computational Physics}, year = {2012}, volume = {11}, number = {3}, pages = {951--984}, 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 O(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. 

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.101010.250511a}, url = {http://global-sci.org/intro/article_detail/cicp/7397.html} }
TY - JOUR T1 - Composite Coherent States Approximation for One-Dimensional Multi-Phased Wave Functions JO - Communications in Computational Physics VL - 3 SP - 951 EP - 984 PY - 2012 DA - 2012/11 SN - 11 DO - http://doi.org/10.4208/cicp.101010.250511a UR - https://global-sci.org/intro/article_detail/cicp/7397.html KW - AB -

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 O(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. 

Dongsheng Yin & Chunxiong Zheng. (2020). Composite Coherent States Approximation for One-Dimensional Multi-Phased Wave Functions. Communications in Computational Physics. 11 (3). 951-984. doi:10.4208/cicp.101010.250511a
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