Quantum Mechanics

by Greiner, Walter

• ISBN13: 9783540600732
• ISBN10: 3540600736
• Edition: 1st
• Format: Paperback
• Copyright: 1998-03-01
• Publisher: Springer Verlag

Summary

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.

Table of Contents

1. Quantum Theory of Free Electromagnetic Fields	1	(30)
1.1 Maxwell's Equations	1	(2)
1.2 Electromagnetic Plane Waves	3	(2)
1.3 Quantization of Free Electromagnetic Fields	5	(7)
1.4 Eigenstates of Electromagnetic Fields	12	(4)
1.5 Coherent States (Glauber States) of Electromagnetic Fields	16	(13)
1.6 Biographical Notes	29	(2)
2. Interaction of Electromagnetic Fields with Matter	31	(50)
2.1 Emission of Radiation from an Excited Atom	33	(2)
2.2 Lifetime of an Excited State	35	(13)
2.3 Absorption of Photons	48	(7)
2.4 Photon Scattering from Free Electrons	55	(2)
2.5 Calculation of the Total Photon Scattering Cross Section	57	(6)
2.6 Cherenkov Radiation of a Schrodinger Electron	63	(11)
2.7 Natural Linewidth and Self-energy	74	(7)
3. Noninteracting Fields	81	(28)
3.1 Spin-Statistics Theorem	98	(1)
3.2 Relationship Between Second Quantization and Elementary Quantum Mechanics	99	(10)
4. Quantum Fields with Interaction	109	(24)
5. Infinities in Quantum Electrodynamics: Renormalization Problems	133	(28)
5.1 Attraction of Parallel, Conducting Plates Due to Field Quantum Fluctuations (Casimir Effect)	133	(10)
5.2 Renormalization of the Electron Mass	143	(6)
5.3 The Splitting of the Hydrogen States 2s(1/2)-2p(3/2): The Lamb Shift	149	(7)
5.4 Is There an Inconsistency in Bethe's Approach?	156	(5)
6. Nonrelativistic Quantum Field Theory of Interacting Particles and Its Applications	161	(32)
6.1 Quantum Gases	165	(9)
6.2 Nearly Ideal, Degenerate Bose-Einstein Gases	174	(19)
7. Superfluidity	193	(20)
7.1 Basics of a Microscopic Theory of Superfluidity	194	(11)
7.2 Landau's Theory of Superfluidity	205	(8)
8. Pair Correlations Among Fermions and Bosons	213	(28)
8.1 Pair-Correlation Function for Fermions	213	(5)
8.2 Pair-Correlation Function for Bosons	218	(5)
8.3 The Hanbury-Brown and Twiss Effect	223	(3)
8.4 Cooper Pairs	226	(15)
9. Quasiparticles in Plasmas and Metals: Selected Topics	241	(14)
9.1 Plasmons and Phonons	246	(9)
10. Basics of Quantum Statistics	255	(30)
10.1 Concept of Quantum Statistics and the Notion of Entropy	255	(1)
10.2 Density Operator of a Many-Particle State	256	(16)
10.3 Dynamics of a Quantum-Statistical Ensemble	272	(4)
10.4 Ordered and Disordered Systems: The Density Operator and Entropy	276	(2)
10.5 Stationary Ensembles	278	(7)
11. Structure of Atoms	285	(50)
11.1 Atoms with Two Electrons	285	(7)
11.2 The Hartree Method	292	(1)
11.3 Thomas-Fermi Method	293	(4)
11.4 The Hartree-Fock Method	297	(8)
11.5 On the Periodic System of the Elements	305	(1)
11.6 Splitting of Orbital Multiplets	306	(6)
11.7 Spin-Orbit Interaction	312	(12)
11.8 Treatment of the Spin-Orbit Splitting in the Hartree-Fock Approach	324	(3)
11.9 The Zeeman Effect	327	(5)
11.10 Biographical Notes	332	(3)
12. Elementary Structure of Molecules	335	(26)
12.1 Born-Oppenheimer Approximation	337	(2)
12.2 The H(+)(2) Ion as an Example	339	(7)
12.3 The Hydrogen Molecule	346	(3)
12.4 Electron Pairing	349	(2)
12.5 Spatially Oriented Orbits	351	(2)
12.6 Hybridization	353	(3)
12.7 Hydrocarbons	356	(2)
12.8 Biographical Notes	358	(3)
13. Feynman's Path Integral Formulation of Schrodinger's Wave Mechanics	361	(16)
13.1 Action Functional in Classical Mechanics and Schrodinger's Wave Mechanics	362	(3)
13.2 Transition Amplitude as a Path Integral	365	(5)
13.3 Path Integral Representation of the Schrodinger Propagator	370	(4)
13.4 Alternative Derivation of the Schrodinger Equation	374	(2)
13.5 Biographical Notes	376	(1)
Subject Index	377