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.Written for advanced-level students and
professors in mathematics and mathematical physics, it is designed
as a complete textbook course providing analysis on the most
important research on the subject to date. Due to the advanced
nature of the content, it is also suitable for research
mathematicians, engineers and chemists active in the field.
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