List of figures List of tables List of definitions, principles, etc. List of boxes List of symbols List of abbreviations Introduction Part I Basic features of quantum mechanics 1 From classical mechanics to quantum mechanics 1.1 Review of the foundations of classical mechanics 1.2 An interferometry experiment and its consequences 1.3 State as vector 1.4 Quantum probability 1.5 The historical need of a new mechanics Summary Problems Further reading 2 Quantum observables and states 2.1 Basic features of quantum observables 2.2 Wave function and basic observables 2.3 Uncertainty relation 2.4 Quantum algebra and quantum logic Summary Problems Further reading 3 Quantum dynamics 3.1 The Schr'6dinger equation 3.2 Properties of the Schrodinger equation 3.3 Schrodinger equation and Galilei transformations 3.4 One-dimensional free particle in a box 3.5 Unitary transformations 3.6 Different pictures 3.7 Time derivatives and the Ehrenfest theorem 3.8 Energy-time uncertainty relation 3.9 Towards a time operator Summary Problems Further reading 4 Examples of quantum dynamics 4.1 Finite potential wells 4.2 Potential barrier 4.3 Tunneling 4.4 Harmonic oscillator 4.5 Quantum particles in simple fields Summary Problems 5 Density matrix 5.1 Basic formalism 5.2 Expectation values and measurement outcomes 5.3 Time evolution and density matrix
5.4 Statistical properties of quantum mechanics 5.5 Compound systems 5.6 Pure- and mixed-state representation Summary Problems Further reading Part II More advanced topics 6 Angular momentum and spin 6.1 Orbital angular momentum 6.2 Special examples 6.3 Spin 6.4 Composition of angular momenta and total angular momentum 6.5 Angular momentum and angle Summary Problems Further reading 7 Identical particles 7.1 Statistics and quantum mechanics 7.2 Wave function and symmetry 7.3 Spin and statistics 7.4 Exchange interaction 7.5 Two recent applications Summary Problems Further reading 8 Symmetries and conservation laws 8.1 Quantum transformations and symmetries 8.2 Continuous symmetries 8.3 Discrete symmetries 8.4 A brief introduction to group theory Summary Problems Further reading 9 The measurement problem in quantum mechanics 9.1 Statement of the problem 9.2 A brief history of the problem 9.3 Schr'odinger cats 9.4 Decoherence 9.5 Reversibility/irreversihility 9.6 Interaction-free measurement 9.7 Delayed-choice experiments 9.8 Quantum Zeno effect 9.9 Conditional measurements or postselection 9.10 Positive operator valued measure 9.11 Quantum non-demolition measurements 9.12 Decision and estimation theory Summary Problems Further reading Part III Matter and light
10 Perturbations and approximation methods 10.1 Stationary perturbation theory 10.2 Time-dependent perturbation theory 10.3 Adiabatic theorem 10.4 The variational method 10.5 Classical limit 10.6 Semiclassical limit and WKB approximation 10.7 Scattering theory 10.8 Path integrals Summary Problems Further reading 11 Hydrogen and helium atoms 11.1 Introduction 11.2 Quantum theory of the hydrogen atom 11.3 Atom and magnetic field 11.4 Relativistic corrections 11.5 Helium atom 11.6 Many-electron effects Summary Problems Further reading 12 Hydrogen molecular ion 12.1 The molecular problem 12.2 Born-Oppenheimer approximation 12.3 Vibrational and rotational degrees of freedom 12.4 The Morse potential 12.5 Chemical bonds and further approximations Summary Problems Further reading 13 Quantum optics 13.1 Quantization of the electromagnetic field 13.2 Thermodynamic equilibrium of the radiation field 13.3 Phase-number uncertainty relation 13.4 Special states of the electromagnetic field 13.5 Quasi-probability distributions 13.6 Quantum-optical coherence 13.7 Atom-field interaction 13.8 Geometric phase 13.9 The Casimir effect Summary Problems Further reading Part IV Quantum information: state and correlations 14 Quantum theory of open systems 14.1 General considerations 14.2 The master equation 14.3 A formal generalization 14.4 Quantum jumps and quantum trajectories
14.5 Quantum optics and Schrodinger cats Summary Problems Further reading 15 State measurement in quantum mechanics 15.1 Protective measurement of the state 15.2 Quantum cloning and unitarity violation 15.3 Measurement and reversibility 15.4 Quantum state reconstruction 15.5 The nature of quantum states Summary Problems Further reading 16 Entanglement: non-separability 16.1 EPR 16.2 Bohm's version of the EPR state 16.3 HV theories 16.4 Bell's contribution 16.5 Experimental tests 16.6 Bell inequalities with homodyne detection 16.7 Bell theorem without inequalities 16.8 What is quantum non-locality? 16.9 Further developments about inequalities 16.10 Conclusion Summary Problems Further reading 17 Entanglement: quantum information and computation 17.1 Information and entropy 17.2 Entanglement and information 17.3 Measurement and information 17.4 Qubits 17.5 Teleportation 17.6 Quantum cryptography 17.7 Elements of quantum computation 17.8 Quantum algorithms and error correction Summary Problems Further reading Bibliography Author index Subject index
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