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Coherent states and applications in ...

Combescure, Monique.

Coherent states and applications in mathematical physics

Record Type:	Electronic resources : Monograph/item
Title/Author:	Coherent states and applications in mathematical physicsby Didier Robert, Monique Combescure.
Author:	Robert, Didier.
other author:	Combescure, Monique.
Published:	Cham :Springer International Publishing :2021.
Description:	xvii, 577 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Coherent states.
Online resource:	https://doi.org/10.1007/978-3-030-70845-0
ISBN:	9783030708450$q(electronic bk.)

Coherent states and applications in mathematical physics
Robert, Didier.

Coherent states and applications in mathematical physics[electronic resource] /by Didier Robert, Monique Combescure. - Second edition. - Cham :Springer International Publishing :2021. - xvii, 577 p. :ill. (some col.), digital ;24 cm. - Theoretical and mathematical physics,1864-5879. - Theoretical and mathematical physics..

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 Schrodinger 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.

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.

ISBN: 9783030708450$q(electronic bk.)

Standard No.: 10.1007/978-3-030-70845-0doiSubjects--Topical Terms:

229767
Coherent states.

LC Class. No.: QC6.4.C56 / R63 2021

Dewey Class. No.: 530.15

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505 0 $a 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 Schrodinger 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.
520 $a 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.
650 0 $a Coherent states. $3 229767
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