Coherent States and Applications in Mathematical Physics

ISBN-13: 9789400701953 / Angielski / Twarda / 2012 / 418 str.

Monique Combescure; Didier Robert

Opis

Intended as a compendium for physicists and mathematicians on coherent states and their applications, this volume moves from the basic mathematical structures of generalized coherent states to specific examples of coherent states such as the hydrogen atom.

Recenzje

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)

Spis treści

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 Schrödinger 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.

Blurb

This book presents the various types of coherent states introduced and studied in the physics and mathematics literature and describes their properties together with application to quantum physics problems. It is intended to serve as a compendium on coherent states and their applications for physicists and mathematicians, stretching from the basic mathematical structures of generalized coherent states in the sense of Perelomov via the semiclassical evolution of coherent states to various specific examples of coherent states (hydrogen atom, quantum oscillator, ...).