QUANTUM MECHANICS Gennaro Auletta Mauro Fortunato Giorgio Parisi :e www.cambridge.org/9780521869638
Quantum Mechanics The important changes quantum mechanics has undergone in recent years are reflected in hisneaprach for A strong narrative and over 300 worked problems lead the student from experiment. through general principles of the theory.to modern applications.Stepping through results allow students to.with bas antum mechan ics,the book moves on to more advanced theory,followed by applications,perturbation methods and special fields,and ending with new developments in the field.Historical, mathematical,and philosophical boxes guide the student through the theory.Unique to this textbook are chapters on measurement and quantum optics.both at the forefront of current research.Advanced undergraduate and graduate students will benefit from this new perspective on the fundamental physical paradigm and its applications. Online resources including solutions to selected problems and 200 figures,with color versions of some figures,are available at www.cambridge.org/Auletta. Gennaro Auletta is Scientific Director of Science and Philosophy at the Pontifical Grego- rian University,Rome.His main areas of research are quantum mechanics,logic,cognitive sciences,information theory,and applications to biological systems. Mauro Fortunato is a Structurer at Cassa depositieprestiti S.p.A..Rome.He is involved in financial engineering,applying mathematical methods of quantum physics to the pricing of complex financial derivatives and the construction of structured products. Giorgio Parisi is Professor of Quantum Theories at the University of Rome"La Sapienza. He has won several prizes,notably the Boltzmann Medal,the Dirac Medal and Prize,and the Daniel Heineman prize.His main research activity deals with elementary particles. very large scale sim behavior
Quantum Mechanics The important changes quantum mechanics has undergone in recent years are reflected in this new approach for students. A strong narrative and over 300 worked problems lead the student from experiment, through general principles of the theory, to modern applications. Stepping through results allows students to gain a thorough understanding. Starting with basic quantum mechanics, the book moves on to more advanced theory, followed by applications, perturbation methods and special fields, and ending with new developments in the field. Historical, mathematical, and philosophical boxes guide the student through the theory. Unique to this textbook are chapters on measurement and quantum optics, both at the forefront of current research. Advanced undergraduate and graduate students will benefit from this new perspective on the fundamental physical paradigm and its applications. Online resources including solutions to selected problems and 200 figures, with color versions of some figures, are available at www.cambridge.org/Auletta. Gennaro Auletta is Scientific Director of Science and Philosophy at the Pontifical Gregorian University, Rome. His main areas of research are quantum mechanics, logic, cognitive sciences, information theory, and applications to biological systems. Mauro Fortunato is a Structurer at Cassa depositi e prestiti S.p.A., Rome. He is involved in financial engineering, applying mathematical methods of quantum physics to the pricing of complex financial derivatives and the construction of structured products. Giorgio Parisi is Professor of Quantum Theories at the University of Rome “La Sapienza.” He has won several prizes, notably the Boltzmann Medal, the Dirac Medal and Prize, and the Daniel Heineman prize. His main research activity deals with elementary particles, theory of phase transitions and statistical mechanics, disordered systems, computers and very large scale simulations, non-equilibrium statistical physics, optimization, and animal behavior
Contents List of figures page xi List of tables List of definitions,principles,etc. xvi List of boxes List of symbols List of abbreviations Introduction Part I Basic features of quantum mechanics 1 From classical mechanics to quantum mechanics 7 1.1 Review of the foundations of classical mechanics 7 10 An interferometry experiment and its consequences 1.3 State as vecto Quantum probability 2028 1.5 The historical need of a new mechanics Summary Problems Further reading 2 Quantum observables and states 3 2.1 Basic features of quantum observables 2.2 Wave function and basic observables 68 2.3 Uncertainty relation 2.4 Quantum algebra and quantum logic Summary 2% Problems Further reading 3 Quantum dynamics 100 3.1 The Schrodinger equation 101 3.2 Properties of the Schrodinger eq ation 107 3.3 One-dimensional free particle in a box 35 Unitary transformations 117
Contents List of figures page xi List of tables xvii List of definitions, principles, etc. xviii List of boxes xx List of symbols xxi List of abbreviations xxxii Introduction 1 Part I Basic features of quantum mechanics 1 From classical mechanics to quantum mechanics 7 1.1 Review of the foundations of classical mechanics 7 1.2 An interferometry experiment and its consequences 12 1.3 State as vector 20 1.4 Quantum probability 28 1.5 The historical need of a new mechanics 31 Summary 40 Problems 41 Further reading 42 2 Quantum observables and states 43 2.1 Basic features of quantum observables 43 2.2 Wave function and basic observables 68 2.3 Uncertainty relation 82 2.4 Quantum algebra and quantum logic 92 Summary 96 Problems 97 Further reading 99 3 Quantum dynamics 100 3.1 The Schrödinger equation 101 3.2 Properties of the Schrödinger equation 107 3.3 Schrödinger equation and Galilei transformations 111 3.4 One-dimensional free particle in a box 113 3.5 Unitary transformations 117
vi Contents 3.6 Different pictures 125 37 Time derivatives and the Ehrenfest theorem 129 8 Energy-time uncertainty relation 39 Towards a time operator 01 Summary 138 Further reading 4 Examples of quantum dynamics 4.1 Finite potential wells 4.2 Potential barrier 4.3 Tunneling 45 4.4 Harmonic oscillator 154 4.5 Quantum particles in simple field Summarv Problems 170 5 Density matrix 5.1 Basic formalism 52 Expectation values and measurement outcomes Tim evolution and density matrix Statistical properties of quantum mechanics 5.5 Compound systems 5.6 Pure-and mixed-state representation mmary Problems Further reading 190 Part ll More advanced topics 6 Angular momentum and spin 6 Orbital angular momentum 6 Speciale amples Spin 0 64 Composition of angular momenta and total angular momentum 226 6.5 Angular momentum and angle 239 Summar Problems Further reading 244 7 Identical particles 245 7.1 Statistics and quantum mechanics 245 7.2 Wave function and symmetry 247 7.3 Spin and statistics 249
vi Contents 3.6 Different pictures 125 3.7 Time derivatives and the Ehrenfest theorem 129 3.8 Energy–time uncertainty relation 130 3.9 Towards a time operator 135 Summary 138 Problems 139 Further reading 140 4 Examples of quantum dynamics 141 4.1 Finite potential wells 141 4.2 Potential barrier 145 4.3 Tunneling 150 4.4 Harmonic oscillator 154 4.5 Quantum particles in simple fields 165 Summary 169 Problems 170 5 Density matrix 174 5.1 Basic formalism 174 5.2 Expectation values and measurement outcomes 177 5.3 Time evolution and density matrix 179 5.4 Statistical properties of quantum mechanics 180 5.5 Compound systems 181 5.6 Pure- and mixed-state representation 187 Summary 188 Problems 189 Further reading 190 Part II More advanced topics 6 Angular momentum and spin 193 6.1 Orbital angular momentum 193 6.2 Special examples 207 6.3 Spin 217 6.4 Composition of angular momenta and total angular momentum 226 6.5 Angular momentum and angle 239 Summary 241 Problems 242 Further reading 244 7 Identical particles 245 7.1 Statistics and quantum mechanics 245 7.2 Wave function and symmetry 247 7.3 Spin and statistics 249
Contents 7.4 Exchange interaction 7.5 Two recent applications Summary 257 Problem Further reading 派 8 Symmetries and conservation laws 259 81 Quantum transformations and symmetries 8.2 Continuous symmetries 83 Discrete symmetries 8.4 A brief introduction to group theory 267 Summary Problems Further reading 276 9 The measurement problem in quantum mechanics 27 9.1 Statement of the problem 9.2 A brief history of the problem 284 93 Schrodinger cats 9.4 Decoherence 9.5 Reversibility/irreversibility 9.6 Interaction-free measurement 315 97 Delayed-choice experim 98 Quantum Zeno effect 9. Conditional measurements or postselection 02 9.10 Positive operator valued measure 9.11 Quantum non-demolition measurements 9.12 Decision and estimation theory Summary 349 Problems 351 Further reading 353 Part Ill Matter and light 10 Perturbations and approximation methods 10.1 Stationary perturbation theory 357 10.2 Time-dependent perturbation theory 36 10.3 Adiabatic theorem 10.4 The variational methoc 10.5 Classical limit 372 106 Semiclassical limit and WKB approximation 10.7 Scattering theory 10.8 Path integrals Summary 398
vii Contents 7.4 Exchange interaction 254 7.5 Two recent applications 255 Summary 257 Problems 257 Further reading 258 8 Symmetries and conservation laws 259 8.1 Quantum transformations and symmetries 259 8.2 Continuous symmetries 264 8.3 Discrete symmetries 266 8.4 A brief introduction to group theory 267 Summary 275 Problems 275 Further reading 276 9 The measurement problem in quantum mechanics 277 9.1 Statement of the problem 278 9.2 A brief history of the problem 284 9.3 Schrödinger cats 291 9.4 Decoherence 297 9.5 Reversibility/irreversibility 308 9.6 Interaction-free measurement 315 9.7 Delayed-choice experiments 320 9.8 Quantum Zeno effect 322 9.9 Conditional measurements or postselection 325 9.10 Positive operator valued measure 327 9.11 Quantum non-demolition measurements 335 9.12 Decision and estimation theory 341 Summary 349 Problems 351 Further reading 353 Part III Matter and light 10 Perturbations and approximation methods 357 10.1 Stationary perturbation theory 357 10.2 Time-dependent perturbation theory 366 10.3 Adiabatic theorem 369 10.4 The variational method 371 10.5 Classical limit 372 10.6 Semiclassical limit and WKB approximation 378 10.7 Scattering theory 384 10.8 Path integrals 389 Summary 398