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Coherent States and Applications in Mathematical Physics


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Table of Contents

The standard coherent states of quantum mechanics.- The Weyl-Heisenberg group and the coherent states of arbitrary profile.- The coherent states of the Harmonic Oscillator.- From Schroedinger to Fock-Bargmann representation.- Weyl quantization and coherent states: Classical and Quantum observables.- Wigner function.- Coherent states and operator norm estimates.- Product rule and applications.- Husimi functions, frequency sets and propagation.- The Wick and anti-Wick quantization.- The generalized coherent states in the sense of Perelomov.- The SU(1,1) coherent states: Definition and properties.- The squeezed states.- The SU(2) coherent states.- The quantum quadratic Hamiltonians: The propagator of quadratic quantum Hamiltonians.- The metaplectic transformations.- The propagation of coherent states.- Representation of the Weyl symbols of the metaplectic operators.- The semiclassical evolution of coherent states.- The van Vleck and Hermann-Kluk approximations.- The semiclassical Gutzwiller trace formula using coherent states decomposition.- The hydrogen atom coherent states: Definition and properties.- The localization around Kepler orbits.- The quantum singular oscillator: The two-body case.- The N-body case.


From the reviews:"This book is meant to be a solid and formal introduction to the theory of coherent states and their applications in mathematical physics ... . Most of the emphasis in this work is concentrated on applications of coherent states to semi-classical analysis, as well as to the mathematical treatment of the theory, hence providing a more consistent formal basis than other monographs on the subject. ... will certainly be very useful for both physicists and mathematicians." (Rutwig Campoamor-Stursberg, Mathematical Reviews, March, 2013)"In this book, the authors elaborate the canonical Gaussian Coherent States and their applications. ... This book is a masterpiece at present. The material covered in this book is designed for an advanced graduate student or researcher. The one-parameter coherent states today have caused a great interest for scholars. The authors introduce well into this topic." (Chen Yong-Qing, Zentralblatt MATH, Vol. 1243, 2012)

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