Year: 2012
Communications in Computational Physics, Vol. 11 (2012), Iss. 3 : pp. 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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.101010.250511a
Communications in Computational Physics, Vol. 11 (2012), Iss. 3 : pp. 951–984
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
-
Gaussian beam methods for the Schrödinger equation with discontinuous potentials
Jin, Shi | Wei, Dongming | Yin, DongshengJournal of Computational and Applied Mathematics, Vol. 265 (2014), Iss. P.199
https://doi.org/10.1016/j.cam.2013.09.028 [Citations: 9] -
The Gaussian beam method for the wigner equation with discontinuous potentials
Yin, Dongsheng | Tang, Min | Jin, ShiInverse Problems & Imaging, Vol. 7 (2013), Iss. 3 P.1051
https://doi.org/10.3934/ipi.2013.7.1051 [Citations: 4] -
Optimal Error Estimates for First-Order Gaussian Beam Approximations to the Schrödinger Equation
Zhen, Chunxiong
SIAM Journal on Numerical Analysis, Vol. 52 (2014), Iss. 6 P.2905
https://doi.org/10.1137/130935720 [Citations: 6]