viⅷi Contents Problems 399 Further reading 11 Hydrogen and helium atoms 401 11.1 Introduction 401 11.2 Quantum theory of the hydrogen atom 403 113 Atom and magnetic field 413 11.4 Relativistic corrections 11.5 Helium atom 11.6 Many-electron effect Summary Problems 437 Further reading 438 12 Hydrogen molecular ion 439 12.1 The molecular problem 439 12.2 Born-Oppenheimer approximation 440 12.3 Vibrational and rotational degrees of freedom 12.4 The Morse potential 12.5 Chemical bonds and further approximations 44g Summary Problems Further reading 454 13 Quantum optics 13.1 Quantization of the electromagnetic field 57 13.2 Thermodynamic equilibrium of the radiation field 462 133 Phase mber ertainty relation 13.4 Special states of the electromagnetic field 465 13.5 Quasi-probability distributions 13.6 Quantum-optical coherence 481 13.7 Atom-field interaction 13.8 Geometric phase 13.9 The Casimir effect 501 Summary 506 Problems Further reading Part IV Quantum information:state and correlations 14 Quantum theory of open systems 513 14.1 General considerations 514 14.2 The master equation 516 viii Contents Problems 399 Further reading 399 11 Hydrogen and helium atoms 401 11.1 Introduction 401 11.2 Quantum theory of the hydrogen atom 403 11.3 Atom and magnetic field 413 11.4 Relativistic corrections 423 11.5 Helium atom 426 11.6 Many-electron effects 431 Summary 436 Problems 437 Further reading 438 12 Hydrogen molecular ion 439 12.1 The molecular problem 439 12.2 Born–Oppenheimer approximation 440 12.3 Vibrational and rotational degrees of freedom 443 12.4 The Morse potential 447 12.5 Chemical bonds and further approximations 449 Summary 453 Problems 453 Further reading 454 13 Quantum optics 455 13.1 Quantization of the electromagnetic field 457 13.2 Thermodynamic equilibrium of the radiation field 462 13.3 Phase–number uncertainty relation 463 13.4 Special states of the electromagnetic field 465 13.5 Quasi-probability distributions 474 13.6 Quantum-optical coherence 481 13.7 Atom–field interaction 484 13.8 Geometric phase 497 13.9 The Casimir effect 501 Summary 506 Problems 507 Further reading 509 Part IV Quantum information: state and correlations 14 Quantum theory of open systems 513 14.1 General considerations 514 14.2 The master equation 516