LEADER 05404nam 2200661Ia 450 001 9910818401003321 005 20240505211555.0 010 $a1-282-30253-1 010 $a9786612302534 010 $a3-527-62828-2 010 $a3-527-62829-0 035 $a(CKB)1000000000799236 035 $a(EBL)482010 035 $a(OCoLC)501317088 035 $a(SSID)ssj0000335928 035 $a(PQKBManifestationID)11257815 035 $a(PQKBTitleCode)TC0000335928 035 $a(PQKBWorkID)10277478 035 $a(PQKB)10652459 035 $a(MiAaPQ)EBC482010 035 $a(Au-PeEL)EBL482010 035 $a(CaPaEBR)ebr10341789 035 $a(CaONFJC)MIL230253 035 $a(PPN)224991612 035 $a(EXLCZ)991000000000799236 100 $a20090804d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCoherent states in quantum physics /$fby Jean-Pierre Gazeau 205 $a1st ed. 210 $aWeinheim $cWiley-VCH$d2009 215 $a1 online resource (360 p.) 300 $a"Originates from a series of advanced lectures on coherent states in physics, delivered in Strasbourg, Louvain-la-Neuve, Paris, Rio de Janeiro, Rabat, and Bialystok, over the period from 1997 to 2008"--Pref. 311 $a3-527-40709-X 320 $aIncludes bibliographical references and index. 327 $aCoherent States in Quantum Physics; Contents; Preface; Part One Coherent States; 1 Introduction; 1.1 The Motivations; 2 The Standard Coherent States: the Basics; 2.1 Schro?dinger Definition; 2.2 Four Representations of Quantum States; 2.2.1 Position Representation; 2.2.2 Momentum Representation; 2.2.3 Number or Fock Representation; 2.2.4 A Little (Lie) Algebraic Observation; 2.2.5 Analytical or Fock-Bargmann Representation; 2.2.6 Operators in Fock-Bargmann Representation; 2.3 Schro?dinger Coherent States; 2.3.1 Bergman Kernel as a Coherent State; 2.3.2 A First Fundamental Property 327 $a2.3.3 Schro?dinger Coherent States in the Two Other Representations2.4 Glauber-Klauder-Sudarshan or Standard Coherent States; 2.5 Why the Adjective Coherent?; 3 The Standard Coherent States: the (Elementary) Mathematics; 3.1 Introduction; 3.2 Properties in the Hilbertian Framework; 3.2.1 A ``Continuity'' from the Classical Complex Plane to Quantum States; 3.2.2 ``Coherent'' Resolution of the Unity; 3.2.3 The Interplay Between the Circle (as a Set of Parameters) and the Plane (as a Euclidean Space); 3.2.4 Analytical Bridge; 3.2.5 Overcompleteness and Reproducing Properties 327 $a3.3 Coherent States in the Quantum Mechanical Context3.3.1 Symbols; 3.3.2 Lower Symbols; 3.3.3 Heisenberg Inequalities; 3.3.4 Time Evolution and Phase Space; 3.4 Properties in the Group-Theoretical Context; 3.4.1 The Vacuum as a Transported Probe...; 3.4.2 Under the Action of...; 3.4.3 ... the D-Function; 3.4.4 Symplectic Phase and the Weyl-Heisenberg Group; 3.4.5 Coherent States as Tools in Signal Analysis; 3.5 Quantum Distributions and Coherent States; 3.5.1 The Density Matrix and the Representation ``R''; 3.5.2 The Density Matrix and the Representation ``Q'' 327 $a3.5.3 The Density Matrix and the Representation ``P''3.5.4 The Density Matrix and the Wigner(-Weyl-Ville) Distribution; 3.6 The Feynman Path Integral and Coherent States; 4 Coherent States in Quantum Information: an Example of Experimental Manipulation; 4.1 Quantum States for Information; 4.2 Optical Coherent States in Quantum Information; 4.3 Binary Coherent State Communication; 4.3.1 Binary Logic with Two Coherent States; 4.3.2 Uncertainties on POVMs; 4.3.3 The Quantum Error Probability or Helstrom Bound; 4.3.4 The Helstrom Bound in Binary Communication 327 $a4.3.5 Helstrom Bound for Coherent States4.3.6 Helstrom Bound with Imperfect Detection; 4.4 The Kennedy Receiver; 4.4.1 The Principle; 4.4.2 Kennedy Receiver Error; 4.5 The Sasaki-Hirota Receiver; 4.5.1 The Principle; 4.5.2 Sasaki-Hirota Receiver Error; 4.6 The Dolinar Receiver; 4.6.1 The Principle; 4.6.2 Photon Counting Distributions; 4.6.3 Decision Criterion of the Dolinar Receiver; 4.6.4 Optimal Control; 4.6.5 Dolinar Hypothesis Testing Procedure; 4.7 The Cook-Martin-Geremia Closed-Loop Experiment; 4.7.1 A Theoretical Preliminary; 4.7.2 Closed-Loop Experiment: the Apparatus 327 $a4.7.3 Closed-Loop Experiment: the Results 330 $aThis self-contained introduction discusses the evolution of the notion of coherent states, from the early works of Schr?dinger to the most recent advances, including signal analysis. An integrated and modern approach to the utility of coherent states in many different branches of physics, it strikes a balance between mathematical and physical descriptions.Split into two parts, the first introduces readers to the most familiar coherent states, their origin, their construction, and their application and relevance to various selected domains of physics. Part II, mostly based on recent origina 606 $aCoherent states 606 $aQuantum theory 615 0$aCoherent states. 615 0$aQuantum theory. 676 $a530.12 700 $aGazeau$b Jean-Pierre$048964 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910818401003321 996 $aCoherent states in quantum physics$94081255 997 $aUNINA