Quantum Mechanics -- Special Chapters is an important additional course for third-year students. Starting with the quantization of a free electromagnetic field and its interaction with matter, it discusses second quantization and interacting quantum fields. After re-normalization problems and a general treatment of nonrelativistic quantum field theory, these methods are applied to problems from solid-state physics and plasma physics: quantum gas, superfluidity, plasmons, and photons. The book concludes with an introduction to quantum statistics, the structure of atoms and molecules, and the…mehr
Quantum Mechanics -- Special Chapters is an important additional course for third-year students. Starting with the quantization of a free electromagnetic field and its interaction with matter, it discusses second quantization and interacting quantum fields. After re-normalization problems and a general treatment of nonrelativistic quantum field theory, these methods are applied to problems from solid-state physics and plasma physics: quantum gas, superfluidity, plasmons, and photons. The book concludes with an introduction to quantum statistics, the structure of atoms and molecules, and the Schrödinger wave equation formulated by Feynman path integrals. 72 fully and carefully worked examples and problems consolidate the material.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
1. Quantum Theory of Free Electromagnetic Fields.- 1.1 Maxwell's Equations.- 1.2 Electromagnetic Plane Waves.- 1.3 Quantization of Free Electromagnetic Fields.- 1.4 Eigenstates of Electromagnetic Fields.- 1.5 Coherent States (Glauber States) of Electromagnetic Fields.- 1.6 Biographical Notes.- 2. Interaction of Electromagnetic Fields with Matter.- 2.1 Emission of Radiation from an Excited Atom.- 2.2 Lifetime of an Excited State.- 2.3 Absorption of Photons.- 2.4 Photon Scattering from Free Electrons.- 2.5 Calculation of the Total Photon Scattering Cross Section.- 2.6 Cherenkov Radiation of a Schrödinger Electron.- 2.7 Natural Linewidth and Self-energy.- 3. Noninteracting Fields.- 3.1 Spin-Statistics Theorem.- 3.2 Relationship Between Second Quantization and Elementary Quantum Mechanics.- 4. Quantum Fields with Interaction.- 5. Infinities in Quantum Electrodynamics: Renormalization Problems.- 5.1 Attraction of Parallel, Conducting Plates Due to Field Quantum Fluctuations (Casimir Effect).- 5.2 Renormalization of the Electron Mass.- 5.3 The Splitting of the Hydrogen States 2s1/2?2p3/2: The Lamb Shift.- 5.4 Is There an Inconsistency in Bethe's Approach?.- 6. Nonrelativistic Quantum Field Theory of Interacting Particles and Its Applications.- 6.1 Quantum Gases.- 6.2 Nearly Ideal, Degenerate Bose-Einstein Gases.- 7. Superfluidity.- 7.1 Basics of a Microscopic Theory of Superfluidity.- 7.2 Landau's Theory of Superfluidity.- 8. Pair Correlations Among Fermions and Bosons.- 8.1 Pair-Correlation Function for Fermions.- 8.2 Pair-Correlation Function for Bosons.- 8.3 The Hanbury-Brown and Twiss Effect.- 8.4 Cooper Pairs.- 9. Quasiparticles in Plasmas and Metals: Selected Topics.- 9.1 Plasmons and Phonons.- 10. Basics of Quantum Statistics.- 10.1 Concept of Quantum Statistics and the Notion of Entropy.- 10.2 Density Operator of a Many-Particle State.- 10.3 Dynamics of a Quantum-Statistical Ensemble.- 10.4 Ordered and Disordered Systems: The Density Operator and Entropy.- 10.5 Stationary Ensembles.- 11. Structure of Atoms.- 11.1 Atoms with Two Electrons.- 11.2 The Hartree Method.- 11.3 Thomas-Fermi Method.- 11.4 The Hartree-Fock Method.- 11.5 On the Periodic System of the Elements.- 11.6 Splitting of Orbital Multiplets.- 11.7 Spin-Orbit Interaction.- 11.8 Treatment of the Spin-Orbit Splitting in the Hartree-Fock Approach.- 11.9 The Zeeman Effect.- 11.10 Biographical Notes.- 12. Elementary Structure of Molecules.- 12.1 Born-Oppenheimer Approximation.- 12.2 The H+2 Ion as an Example.- 12.3 The Hydrogen Molecule.- 12.4 Electron Pairing.- 12.5 Spatially Oriented Orbits.- 12.6 Hybridization.- 12.7 Hydrocarbons.- 12.8 Biographical Notes.- 13. Feynman's Path Integral Formulation of Schrödinger's Wave Mechanics.- 13.1 Action Functional in Classical Mechanics and Schrödinger's Wave Mechanics.- 13.2 Transition Amplitude as a Path Integral.- 13.3 Path Integral Representation of the Schrödinger Propagator.- 13.4 Alternative Derivation of the Schrödinger Equation.- 13.5 Biographical Notes.
1. Quantum Theory of Free Electromagnetic Fields.- 1.1 Maxwell's Equations.- 1.2 Electromagnetic Plane Waves.- 1.3 Quantization of Free Electromagnetic Fields.- 1.4 Eigenstates of Electromagnetic Fields.- 1.5 Coherent States (Glauber States) of Electromagnetic Fields.- 1.6 Biographical Notes.- 2. Interaction of Electromagnetic Fields with Matter.- 2.1 Emission of Radiation from an Excited Atom.- 2.2 Lifetime of an Excited State.- 2.3 Absorption of Photons.- 2.4 Photon Scattering from Free Electrons.- 2.5 Calculation of the Total Photon Scattering Cross Section.- 2.6 Cherenkov Radiation of a Schrödinger Electron.- 2.7 Natural Linewidth and Self-energy.- 3. Noninteracting Fields.- 3.1 Spin-Statistics Theorem.- 3.2 Relationship Between Second Quantization and Elementary Quantum Mechanics.- 4. Quantum Fields with Interaction.- 5. Infinities in Quantum Electrodynamics: Renormalization Problems.- 5.1 Attraction of Parallel, Conducting Plates Due to Field Quantum Fluctuations (Casimir Effect).- 5.2 Renormalization of the Electron Mass.- 5.3 The Splitting of the Hydrogen States 2s1/2?2p3/2: The Lamb Shift.- 5.4 Is There an Inconsistency in Bethe's Approach?.- 6. Nonrelativistic Quantum Field Theory of Interacting Particles and Its Applications.- 6.1 Quantum Gases.- 6.2 Nearly Ideal, Degenerate Bose-Einstein Gases.- 7. Superfluidity.- 7.1 Basics of a Microscopic Theory of Superfluidity.- 7.2 Landau's Theory of Superfluidity.- 8. Pair Correlations Among Fermions and Bosons.- 8.1 Pair-Correlation Function for Fermions.- 8.2 Pair-Correlation Function for Bosons.- 8.3 The Hanbury-Brown and Twiss Effect.- 8.4 Cooper Pairs.- 9. Quasiparticles in Plasmas and Metals: Selected Topics.- 9.1 Plasmons and Phonons.- 10. Basics of Quantum Statistics.- 10.1 Concept of Quantum Statistics and the Notion of Entropy.- 10.2 Density Operator of a Many-Particle State.- 10.3 Dynamics of a Quantum-Statistical Ensemble.- 10.4 Ordered and Disordered Systems: The Density Operator and Entropy.- 10.5 Stationary Ensembles.- 11. Structure of Atoms.- 11.1 Atoms with Two Electrons.- 11.2 The Hartree Method.- 11.3 Thomas-Fermi Method.- 11.4 The Hartree-Fock Method.- 11.5 On the Periodic System of the Elements.- 11.6 Splitting of Orbital Multiplets.- 11.7 Spin-Orbit Interaction.- 11.8 Treatment of the Spin-Orbit Splitting in the Hartree-Fock Approach.- 11.9 The Zeeman Effect.- 11.10 Biographical Notes.- 12. Elementary Structure of Molecules.- 12.1 Born-Oppenheimer Approximation.- 12.2 The H+2 Ion as an Example.- 12.3 The Hydrogen Molecule.- 12.4 Electron Pairing.- 12.5 Spatially Oriented Orbits.- 12.6 Hybridization.- 12.7 Hydrocarbons.- 12.8 Biographical Notes.- 13. Feynman's Path Integral Formulation of Schrödinger's Wave Mechanics.- 13.1 Action Functional in Classical Mechanics and Schrödinger's Wave Mechanics.- 13.2 Transition Amplitude as a Path Integral.- 13.3 Path Integral Representation of the Schrödinger Propagator.- 13.4 Alternative Derivation of the Schrödinger Equation.- 13.5 Biographical Notes.
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