Titre :	Consistent quantum theory
Type de document :	texte imprimé
Auteurs :	Griffiths, Robert B.
Editeur :	Cambridge : Cambridge university press
Année de publication :	2001
Importance :	1 vol. (391 p.)
Format :	24 cm
ISBN/ISSN/EAN :	978-0-521-80349-6
Note générale :	0-521-80349-7
Catégories :	Mathématique
Mots-clés :	Théorie quantique
Index. décimale :	510 Mathématique
Résumé :	Ce volume élucide l'approche cohérente de la théorie quantique en mécanique quantique à un niveau accessible aux étudiants universitaires en physique, chimie, mathématiques et informatique, ce qui en fait un complément idéal aux manuels classiques. Griffiths fournit une explication claire des points qui ne sont pas encore suffisamment enseignés dans les textes traditionnels et que les étudiants trouvent déroutants, de même que leurs enseignants. Le livre intéressera également les physiciens et les philosophes travaillant sur les fondements de la mécanique quantique
Note de contenu :	Sommaire Introduction 1 1.1 Scope of this book 1 1.2 Quantum states and variables 2 1.3 Quantum dynamics 3 1.4 Mathematics I. Linear algebra 4 1.5 Mathematics II. Calculus, probability theory 5 1.6 Quantum reasoning 6 1.7 Quantum measurements 8 1.8 Quantum paradoxes 9 2 Wave functions 11 2.1 Classical and quantum particles 11 2.2 Physical interpretation of the wave function 13 2.3 Wave functions and position 17 2.4 Wave functions and momentum 20 2.5 Toy model 23 3 Linear algebra in Dirac notation 27 3.1 Hilbert space and inner product 27 3.2 Linear functionals and the dual space 29 3.3 Operators, dyads 30 3.4 Projectors and subspaces 34 3.5 Orthogonal projectors and orthonormal bases 36 3.6 Column vectors, row vectors, and matrices 38 3.7 Diagonalization of Hermitian operators 40 3.8 Trace 42 3.9 Positive operators and density matrices 43 vii viii Contents 3.10 Functions of operators 45 4 Physical properties 47 4.1 Classical and quantum properties 47 4.2 Toy model and spin half 48 4.3 Continuous quantum systems 51 4.4 Negation of properties (NOT) 54 4.5 Conjunction and disjunction (AND, OR) 57 4.6 Incompatible properties 60 5 Probabilities and physical variables 65 5.1 Classical sample space and event algebra 65 5.2 Quantum sample space and event algebra 68 5.3 Refinement, coarsening, and compatibility 71 5.4 Probabilities and ensembles 73 5.5 Random variables and physical variables 76 5.6 Averages 79 6 Composite systems and tensor products 81 6.1 Introduction 81 6.2 Definition of tensor products 82 6.3 Examples of composite quantum systems 85 6.4 Product operators 87 6.5 General operators, matrix elements, partial traces 89 6.6 Product properties and product of sample spaces 92 7 Unitary dynamics 94 7.1 The Schrodinger equation 94 ¨ 7.2 Unitary operators 99 7.3 Time development operators 100 7.4 Toy models 102 8 Stochastic histories 108 8.1 Introduction 108 8.2 Classical histories 109 8.3 Quantum histories 111 8.4 Extensions and logical operations on histories 112 8.5 Sample spaces and families of histories 116 8.6 Refinements of histories 118 8.7 Unitary histories 119 9 The Born rule 121 9.1 Classical random walk 121 Contents ix 9.2 Single-time probabilities 124 9.3 The Born rule 126 9.4 Wave function as a pre-probability 129 9.5 Application: Alpha decay 131 9.6 Schrodinger ¨ ’s cat 134 10 Consistent histories 137 10.1 Chain operators and weights 137 10.2 Consistency conditions and consistent families 140 10.3 Examples of consistent and inconsistent families 143 10.4 Refinement and compatibility 146 11 Checking consistency 148 11.1 Introduction 148 11.2 Support of a consistent family 148 11.3 Initial and final projectors 149 11.4 Heisenberg representation 151 11.5 Fixed initial state 152 11.6 Initial pure state. Chain kets 154 11.7 Unitary extensions 155 11.8 Intrinsically inconsistent histories 157 12 Examples of consistent families 159 12.1 Toy beam splitter 159 12.2 Beam splitter with detector 165 12.3 Time-elapse detector 169 12.4 Toy alpha decay 171 13 Quantum interference 174 13.1 Two-slit and Mach–Zehnder interferometers 174 13.2 Toy Mach–Zehnder interferometer 178 13.3 Detector in output of interferometer 183 13.4 Detector in internal arm of interferometer 186 13.5 Weak detectors in internal arms 188 14 Dependent (contextual) events 192 14.1 An example 192 14.2 Classical analogy 193 14.3 Contextual properties and conditional probabilities 195 14.4 Dependent events in histories 196 15 Density matrices 202 15.1 Introduction 202 x Contents 15.2 Density matrix as a pre-probability 203 15.3 Reduced density matrix for subsystem 204 15.4 Time dependence of reduced density matrix 207 15.5 Reduced density matrix as initial condition 209 15.6 Density matrix for isolated system 211 15.7 Conditional density matrices 213 16 Quantum reasoning 216 16.1 Some general principles 216 16.2 Example: Toy beam splitter 219 16.3 Internal consistency of quantum reasoning 222 16.4 Interpretation of multiple frameworks 224 17 Measurements I 228 17.1 Introduction 228 17.2 Microscopic measurement 230 17.3 Macroscopic measurement, first version 233 17.4 Macroscopic measurement, second version 236 17.5 General destructive measurements 240 18 Measurements II 243 18.1 Beam splitter and successive measurements 243 18.2 Wave function collapse 246 18.3 Nondestructive Stern–Gerlach measurements 249 18.4 Measurements and incompatible families 252 18.5 General nondestructive measuremen Contents xi 21.3 Comparing Min and Mout 287 21.4 Delayed choice version 290 21.5 Interaction-free measurement? 293 21.6 Conclusion 295 22 Incompatibility paradoxes 296 22.1 Simultaneous values 296 22.2 Value functionals 298 22.3 Paradox of two spins 299 22.4 Truth functionals 301 22.5 Paradox of three boxes 304 22.6 Truth functionals for histories 308 23 Singlet state correlations 310 23.1 Introduction 310 23.2 Spin correlations 311 23.3 Histories for three times 313 23.4 Measurements of one spin 315 23.5 Measurements of two spins 319 24 EPR paradox and Bell inequalities 323 24.1 Bohm version of the EPR paradox 323 24.2 Counterfactuals and the EPR paradox 326 24.3 EPR and hidden variables 329 24.4 Bell inequalities 332 25 Hardy’s paradox 336 25.1 Introduction 336 25.2 The first paradox 338 25.3 Analysis of the first paradox 341 25.4 The second paradox 343 25.5 Analysis of the second paradox 344 26 Decoherence and the classical limit 349 26.1 Introduction 349 26.2 Particle in an interferometer 350 26.3 Density matrix 352 26.4 Random environment 354 26.5 Consistency of histories 356 26.6 Decoherence and classical physics 356 27 Quantum theory and reality 360 27.1 Introduction 360 xii Contents 27.2 Quantum vs. classical reality 361 27.3 Multiple incompatible descriptions 362 27.4 The macroscopic world 365 27.5 Conclusion 368 Bibliography 371 References 377 Index
Côte titre :	Fs/13382-13383

Consistent quantum theory [texte imprimé] / Griffiths, Robert B. . - Cambridge : Cambridge university press, 2001 . - 1 vol. (391 p.) ; 24 cm.
ISBN : 978-0-521-80349-6
0-521-80349-7

Catégories :	Mathématique
Mots-clés :	Théorie quantique
Index. décimale :	510 Mathématique
Résumé :	Ce volume élucide l'approche cohérente de la théorie quantique en mécanique quantique à un niveau accessible aux étudiants universitaires en physique, chimie, mathématiques et informatique, ce qui en fait un complément idéal aux manuels classiques. Griffiths fournit une explication claire des points qui ne sont pas encore suffisamment enseignés dans les textes traditionnels et que les étudiants trouvent déroutants, de même que leurs enseignants. Le livre intéressera également les physiciens et les philosophes travaillant sur les fondements de la mécanique quantique
Note de contenu :	Sommaire Introduction 1 1.1 Scope of this book 1 1.2 Quantum states and variables 2 1.3 Quantum dynamics 3 1.4 Mathematics I. Linear algebra 4 1.5 Mathematics II. Calculus, probability theory 5 1.6 Quantum reasoning 6 1.7 Quantum measurements 8 1.8 Quantum paradoxes 9 2 Wave functions 11 2.1 Classical and quantum particles 11 2.2 Physical interpretation of the wave function 13 2.3 Wave functions and position 17 2.4 Wave functions and momentum 20 2.5 Toy model 23 3 Linear algebra in Dirac notation 27 3.1 Hilbert space and inner product 27 3.2 Linear functionals and the dual space 29 3.3 Operators, dyads 30 3.4 Projectors and subspaces 34 3.5 Orthogonal projectors and orthonormal bases 36 3.6 Column vectors, row vectors, and matrices 38 3.7 Diagonalization of Hermitian operators 40 3.8 Trace 42 3.9 Positive operators and density matrices 43 vii viii Contents 3.10 Functions of operators 45 4 Physical properties 47 4.1 Classical and quantum properties 47 4.2 Toy model and spin half 48 4.3 Continuous quantum systems 51 4.4 Negation of properties (NOT) 54 4.5 Conjunction and disjunction (AND, OR) 57 4.6 Incompatible properties 60 5 Probabilities and physical variables 65 5.1 Classical sample space and event algebra 65 5.2 Quantum sample space and event algebra 68 5.3 Refinement, coarsening, and compatibility 71 5.4 Probabilities and ensembles 73 5.5 Random variables and physical variables 76 5.6 Averages 79 6 Composite systems and tensor products 81 6.1 Introduction 81 6.2 Definition of tensor products 82 6.3 Examples of composite quantum systems 85 6.4 Product operators 87 6.5 General operators, matrix elements, partial traces 89 6.6 Product properties and product of sample spaces 92 7 Unitary dynamics 94 7.1 The Schrodinger equation 94 ¨ 7.2 Unitary operators 99 7.3 Time development operators 100 7.4 Toy models 102 8 Stochastic histories 108 8.1 Introduction 108 8.2 Classical histories 109 8.3 Quantum histories 111 8.4 Extensions and logical operations on histories 112 8.5 Sample spaces and families of histories 116 8.6 Refinements of histories 118 8.7 Unitary histories 119 9 The Born rule 121 9.1 Classical random walk 121 Contents ix 9.2 Single-time probabilities 124 9.3 The Born rule 126 9.4 Wave function as a pre-probability 129 9.5 Application: Alpha decay 131 9.6 Schrodinger ¨ ’s cat 134 10 Consistent histories 137 10.1 Chain operators and weights 137 10.2 Consistency conditions and consistent families 140 10.3 Examples of consistent and inconsistent families 143 10.4 Refinement and compatibility 146 11 Checking consistency 148 11.1 Introduction 148 11.2 Support of a consistent family 148 11.3 Initial and final projectors 149 11.4 Heisenberg representation 151 11.5 Fixed initial state 152 11.6 Initial pure state. Chain kets 154 11.7 Unitary extensions 155 11.8 Intrinsically inconsistent histories 157 12 Examples of consistent families 159 12.1 Toy beam splitter 159 12.2 Beam splitter with detector 165 12.3 Time-elapse detector 169 12.4 Toy alpha decay 171 13 Quantum interference 174 13.1 Two-slit and Mach–Zehnder interferometers 174 13.2 Toy Mach–Zehnder interferometer 178 13.3 Detector in output of interferometer 183 13.4 Detector in internal arm of interferometer 186 13.5 Weak detectors in internal arms 188 14 Dependent (contextual) events 192 14.1 An example 192 14.2 Classical analogy 193 14.3 Contextual properties and conditional probabilities 195 14.4 Dependent events in histories 196 15 Density matrices 202 15.1 Introduction 202 x Contents 15.2 Density matrix as a pre-probability 203 15.3 Reduced density matrix for subsystem 204 15.4 Time dependence of reduced density matrix 207 15.5 Reduced density matrix as initial condition 209 15.6 Density matrix for isolated system 211 15.7 Conditional density matrices 213 16 Quantum reasoning 216 16.1 Some general principles 216 16.2 Example: Toy beam splitter 219 16.3 Internal consistency of quantum reasoning 222 16.4 Interpretation of multiple frameworks 224 17 Measurements I 228 17.1 Introduction 228 17.2 Microscopic measurement 230 17.3 Macroscopic measurement, first version 233 17.4 Macroscopic measurement, second version 236 17.5 General destructive measurements 240 18 Measurements II 243 18.1 Beam splitter and successive measurements 243 18.2 Wave function collapse 246 18.3 Nondestructive Stern–Gerlach measurements 249 18.4 Measurements and incompatible families 252 18.5 General nondestructive measuremen Contents xi 21.3 Comparing Min and Mout 287 21.4 Delayed choice version 290 21.5 Interaction-free measurement? 293 21.6 Conclusion 295 22 Incompatibility paradoxes 296 22.1 Simultaneous values 296 22.2 Value functionals 298 22.3 Paradox of two spins 299 22.4 Truth functionals 301 22.5 Paradox of three boxes 304 22.6 Truth functionals for histories 308 23 Singlet state correlations 310 23.1 Introduction 310 23.2 Spin correlations 311 23.3 Histories for three times 313 23.4 Measurements of one spin 315 23.5 Measurements of two spins 319 24 EPR paradox and Bell inequalities 323 24.1 Bohm version of the EPR paradox 323 24.2 Counterfactuals and the EPR paradox 326 24.3 EPR and hidden variables 329 24.4 Bell inequalities 332 25 Hardy’s paradox 336 25.1 Introduction 336 25.2 The first paradox 338 25.3 Analysis of the first paradox 341 25.4 The second paradox 343 25.5 Analysis of the second paradox 344 26 Decoherence and the classical limit 349 26.1 Introduction 349 26.2 Particle in an interferometer 350 26.3 Density matrix 352 26.4 Random environment 354 26.5 Consistency of histories 356 26.6 Decoherence and classical physics 356 27 Quantum theory and reality 360 27.1 Introduction 360 xii Contents 27.2 Quantum vs. classical reality 361 27.3 Multiple incompatible descriptions 362 27.4 The macroscopic world 365 27.5 Conclusion 368 Bibliography 371 References 377 Index
Côte titre :	Fs/13382-13383