Coherent states and applications in mathematical physics / Didier Robert, Monique Combescure.
Robert, Didier, author.; Combescure, Monique, author.
2021
QC6.4.C56
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Title
Coherent states and applications in mathematical physics / Didier Robert, Monique Combescure.
Author
Robert, Didier, author.
Edition
Second edition.
ISBN
9783030708450 (electronic bk.)
3030708454 (electronic bk.)
9783030708467 (print)
3030708462
9783030708474 (print)
3030708470
9783030708443 (print)
3030708446
DOI
https://doi.org/10.1007/978-3-030-70845-0
Published
Cham, Switzerland : Springer, [2021]
Language
English
Description
1 online resource (xvii, 577 pages) : illustrations (some color)
Item Number
10.1007/978-3-030-70845-0 doi
Call Number
QC6.4.C56
Dewey Decimal Classification
530.15
Summary
This second edition of the outstanding monograph on coherent states by Combescure and Robert published in 2012 is enriched with figures, historical information and numerical simulations and enlarged with five new chapters presenting important rigorous results obtained in the recent years. The new chapters include various applications such as to the time dependent Schroedinger equation and the Ehrenfest time, to the growth of norms and energy exchanges, to chaotic systems and classical systems with quantum ergodic behavior, and to open quantum systems, and to adiabatic decoupling for multicomponent systems Overall, 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, etc.). It goes beyond existing books on coherent states in terms of a rigorous mathematical framework.
Bibliography, etc. Note
Includes bibliographical references and indexes.
Access Note
Access limited to authorized users.
Digital File Characteristics
text file
PDF
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed June 2, 2021).
Added Author
Combescure, Monique, author.
Series
Theoretical and mathematical physics (Springer (Firm)), 1864-5879
Available in Other Form
Coherent states and applications in mathematical physics.
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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.

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