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Wigner transform / Maurice de Gosson.

By: Material type: TextTextSeries: Advanced textbooks in mathematicsPublication details: New Jersey : World Scientific, ©2017.Description: xx, 229 pages ; 24 cmISBN:
  • 9781786343093 (pbk : alk. paper)
Subject(s): DDC classification:
  • 530.1595 23 G681
Contents:
1. Phase space translations and reflections -- 2. The cross-wigner transform -- 3. The Cross-Ambiguity function -- 4. Weyl operators -- 5. Symplectic covariance -- 6. The moyal identity -- 7. The feichtinger algebra -- 8. The cohen class -- 9. Gaussians and Hermite functions -- 10. Sub-Gaussian estimates -- 11. Moyal star product and twisted convolution -- 12. Probabilistic interpretation of the Wigner transform -- 13. Mixed quantum states and the density operator -- 14. The KLM coditions and the Narcowich-Wigner spectrum -- 15. Wigner transform and quantum blobs -- Appendices.
Summary: This book provides an in-depth and rigorous study of the Wigner transform and its variants. They are presented first within a context of a general mathematical framework, and then through applications to quantum mechanics. The Wigner transform was introduced by Eugene Wigner in 1932 as a probability quasi-distribution which allows expression of quantum mechanical expectation values in the same form as the averages of classical statistical mechanics. It is also used in signal processing as a transform in time-frequency analysis, closely related to the windowed Gabor transform.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 530.1595 G681 (Browse shelf(Opens below)) Available 138031
Total holds: 0

Includes bibliographical references and index.

1. Phase space translations and reflections --
2. The cross-wigner transform --
3. The Cross-Ambiguity function --
4. Weyl operators --
5. Symplectic covariance --
6. The moyal identity --
7. The feichtinger algebra --
8. The cohen class --
9. Gaussians and Hermite functions --
10. Sub-Gaussian estimates --
11. Moyal star product and twisted convolution --
12. Probabilistic interpretation of the Wigner transform --
13. Mixed quantum states and the density operator --
14. The KLM coditions and the Narcowich-Wigner spectrum --
15. Wigner transform and quantum blobs --
Appendices.

This book provides an in-depth and rigorous study of the Wigner transform and its variants. They are presented first within a context of a general mathematical framework, and then through applications to quantum mechanics. The Wigner transform was introduced by Eugene Wigner in 1932 as a probability quasi-distribution which allows expression of quantum mechanical expectation values in the same form as the averages of classical statistical mechanics. It is also used in signal processing as a transform in time-frequency analysis, closely related to the windowed Gabor transform.

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