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