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 l.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 l.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 Schrodinger 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 Schrodinger cats 9.4 Decoherence 9.5 Reversibility/irreversibility 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 …… Part Ⅱ More advanced topics PartⅢ Matter and light Part Ⅳ Ouantum information:state and correlations
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