Quantum mechanics is arguably one of the most successful scientific
theories ever and its applications to chemistry, optics, and
information theory are innumerable. This book provides the reader
with a rigorous treatment of the main mathematical tools from
harmonic analysis which play an essential role in the modern
formulation of quantum mechanics. This allows us at the same time
to suggest some new ideas and methods, with a special focus on
topics such as the Wigner phase space formalism and its
applications to the theory of the density operator and its
entanglement properties. This book can be used with profit by
advanced undergraduate students in mathematics and physics, as well
as by confirmed researchers.
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