|
| 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 |
|  |
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