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Advanced Quantum Mechanics Fourth Edition 2008 [Kietas viršelis]

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  • Formatas: Hardback, 405 pages, aukštis x plotis: 235x155 mm, weight: 1700 g, XVII, 405 p. With 104 Problems., 1 Hardback
  • Išleidimo metai: 12-Aug-2008
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540850619
  • ISBN-13: 9783540850618
Kitos knygos pagal šią temą:
Advanced Quantum Mechanics Fourth Edition 2008Didesnis paveikslėlis
  • Formatas: Hardback, 405 pages, aukštis x plotis: 235x155 mm, weight: 1700 g, XVII, 405 p. With 104 Problems., 1 Hardback
  • Išleidimo metai: 12-Aug-2008
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540850619
  • ISBN-13: 9783540850618
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783540850618.html
Raktažodžiai:
Advanced Quantum Mechanics, the second volume on quantum mechanics by Franz Schwabl, discusses nonrelativistic multi-particle systems, relativistic wave equations and relativistic quantum fields. Characteristic of the author“s work are the comprehensive mathematical discussions in which all intermediate steps are derived and where numerous examples of application and exercises help the reader gain a thorough working knowledge of the subject. The topics treated in the book lay the foundation for advanced studies in solid-state physics, nuclear and elementary particle physics. This text both extends and complements Schwabl“s introductory Quantum Mechanics, which covers nonrelativistic quantum mechanics and offers a short treatment of the quantization of the radiation field. The fourth edition has been thoroughly revised with new material having been added. Furthermore, the layout of the figures has been unified, which should facilitate comprehension.
Part I. Nonrelativistic Many-Particle Systems
1. Second Quantization
3
1.1 Identical Particles, Many-Particle States, and Permutation Symmetry
3
1.1.1 States and Observables of Identical Particles
3
1.1.2 Examples
6
1.2 Completely Symmetric and Antisymmetric States
8
1.3 Bosons
10
1.3.1 States, Fock Space, Creation and Annihilation Operators
10
1.3.2 The Particle-Number Operator
13
1.3.3 General Single- and Many-Particle Operators
14
1.4 Fermions
16
1.4.1 States, Fock Space, Creation and Annihilation Operators
16
1.4.2 Single- and Many-Particle Operators
19
1.5 Field Operators
20
1.5.1 Transformations Between Different Basis Systems
20
1.5.2 Field Operators
21
1.5.3 Field Equations
23
1.6 Momentum Representation
25
1.6.1 Momentum Eigenfunctions and the Hamiltonian
25
1.6.2 Fourier Transformation of the Density
27
1.6.3 The Inclusion of Spin
27
Problems
29
2. Spin-1/2 Fermions
33
2.1 Noninteracting Fermions
33
2.1.1 The Fermi Sphere, Excitations
33
2.1.2 Single-Particle Correlation Function
35
2.1.3 Pair Distribution Function
36
2.1.4 Pair Distribution Function, Density Correlation Functions, and Structure Factor
39
2.2 Ground State Energy and Elementary Theory of the Electron Gas
41
2.2.1 Hamiltonian
41
2.2.2 Ground State Energy in the Hartree—Fock Approximation
42
2.2.3 Modification of Electron Energy Levels due to the Coulomb Interaction
46
2.3 Hartree—Fock Equations for Atoms
49
Problems
52
3. Bosons
55
3.1 Free Bosons
55
3.1.1 Pair Distribution Function for Free Bosons
55
3.1.2 Two-Particle States of Bosons
57
3.2 Weakly Interacting, Dilute Bose Gas
60
3.2.1 Quantum Fluids and Bose—Einstein Condensation
60
3.2.2 Bogoliubov Theory of the Weakly Interacting Bose Gas
62
3.2.3 Superfluidity
69
Problems
72
4. Correlation Functions, Scattering, and Response
75
4.1 Scattering and Response
75
4.2 Density Matrix, Correlation Functions
82
4.3 Dynamical Susceptibility
85
4.4 Dispersion Relations
89
4.5 Spectral Representation
90
4.6 Fluctuation—Dissipation Theorem
91
4.7 Examples of Applications
93
4.8 Symmetry Properties
100
4.8.1 General Symmetry Relations
100
4.8.2 Symmetry Properties of the Response Function for Hermitian Operators
102
4.9 Sum Rules
107
4.9.1 General Structure of Sum Rule
107
4.9.2 Application to the Excitations in He II
108
Problems
109
Bibliography for Part I
111
Part II. Relativistic Wave Equations
5. Relativistic Wave Equations and their Derivation
115
5.1 Introduction
115
5.2 The Klein-Gordon Equation
116
5.2.1 Derivation by Means of the Correspondence Principle
116
5.2.2 The Continuity Equation
119
5.2.3 Free Solutions of the Klein-Gordon Equation
120
5.3 Dirac Equation
120
5.3.1 Derivation of the Dirac Equation
120
5.3.2 The Continuity Equation
122
5.3.3 Properties of the Dirac Matrices
123
5.3.4 The Dirac Equation in Covariant Form
123
5.3.5 Nonrelativistic Limit and Coupling to the Electromagnetic Field
125
Problems
130
6. Lorentz Transformations and Covariance of the Dirac Equation
131
6.1 Lorentz Transformations
131
6.2 Lorentz Covariance of the Dirac Equation
135
6.2.1 Lorentz Covariance and Transformation of Spinors
135
6.2.2 Determination of the Representation S(Λ)
136
6.2.3 Further Properties of S
142
6.2.4 Transformation of Bilinear Forms
144
6.2.5 Properties of the γ Matrices
145
6.3 Solutions of the Dirac Equation for Free Particles
146
6.3.1 Spinors with Finite Momentum
146
6.3.2 Orthogonality Relations and Density
149
6.3.3 Projection Operators
151
Problems
152
7. Orbital Angular Momentum and Spin
155
7.1 Passive and Active Transformations
155
7.2 Rotations and Angular Momentum
156
Problems
159
8. The Coulomb Potential
161
8.1 Klein-Gordon Equation with Electromagnetic Field
161
8.1.1 Coupling to the Electromagnetic Field
161
8.1.2 Klein-Gordon Equation in a Coulomb Field
162
8.2 Dirac Equation for the Coulomb Potential
168
Problems
180
9. The Foldy–Wouthuysen Transformation and Relativistic Corrections
181
9.1 The Foldy -Wouthuysen Transformation
181
9.1.1 Description of the Problem
181
9.1.2 Transformation for Free Particles
182
9.1.3 Interaction with the Electromagnetic Field
183
9.2 Relativistic Corrections and the Lamb Shift
187
9.2.1 Relativistic Corrections
187
9.2.2 Estimate of the Lamb Shift
189
Problems
193
10. Physical Interpretation of the Solutions to the Dirac Equation
195
10.1 Wave Packets and "Zitterbewegung"
195
10.1.1 Superposition of Positive Energy States
196
10.1.2 The General Wave Packet
197
10.1.3 General Solution of the Free Dirac Equation in the Heisenberg Representation
200
10.1.4 Potential Steps and the Klein Paradox
202
10.2 The Hole Theory
204
Problems
207
11. Symmetries and Further Properties of the Dirac Equation
209
11.1 Active and Passive Transformations, Transformations of Vectors
209
11.2 Invariance and Conservation Laws
212
11.2.1 The General Transformation
212
11.2.2 Rotations
212
11.2.3 Translations
213
11.2.4 Spatial Reflection (Parity Transformation)
213
11.3 Charge Conjugation
214
11.4 Time Reversal (Motion Reversal)
217
11.4.1 Reversal of Motion in Classical Physics
218
11.4.2 Time Reversal in Quantum Mechanics
221
11.4.3 Time-Reversal Invariance of the Dirac Equation
229
11.4.4 Racah Time Reflection
235
11.5 Helicity
236
11.6 Zero-Mass Fermions (Neutrinos)
239
Problems
244
Bibliography for Part II
245
Part III. Relativistic Fields
12. Quantization of Relativistic Fields
249
12.1 Coupled Oscillators, the Linear Chain, Lattice Vibrations
249
12.1.1 Linear Chain of Coupled Oscillators
249
12.1.2 Continuum Limit, Vibrating String
255
12.1.3 Generalization to Three Dimensions, Relationship to the Klein—Gordon Field
258
12.2 Classical Field Theory
261
12.2.1 Lagrangian and Euler—Lagrange Equations of Motion
261
12.3 Canonical Quantization
266
12.4 Symmetries and Conservation Laws, Noether's Theorem
266
12.4.1 The Energy—Momentum Tensor, Continuity Equations, and Conservation Laws
266
12.4.2 Derivation from Noether's Theorem of the Conservation Laws for Four-Momentum, Angular Momentum, and Charge
268
Problems
275
13. Free Fields
277
13.1 The Real Klein—Gordon Field
277
13.1.1 The Lagrangian Density, Commutation Relations, and the Hamiltonian
277
13.1.2 Propagators
281
13.2 The Complex Klein—Gordon Field
285
13.3 Quantization of the Dirac Field
287
13.3.1 Field Equations
287
13.3.2 Conserved Quantities
289
13.3.3 Quantization
290
13.3.4 Charge
293
13.3.5 The Infinite-Volume Limit
295
13.4 The Spin Statistics Theorem
296
13.4.1 Propagators and the Spin Statistics Theorem
296
13.4.2 Further Properties of Anticommutators and Propagators of the Dirac Field
301
Problems
303
14. Quantization of the Radiation Field
307
14.1 Classical Electrodynamics
307
14.1.1 Maxwell Equations
307
14.1.2 Gauge Transformations
309
14.2 The Coulomb Gauge
309
14.3 The Lagrangian Density for the Electromagnetic Field
311
14.4 The Free Electromagnatic Field and its Quantization
312
14.5 Calculation of the Photon Propagator
316
Problems
320
15. Interacting Fields, Quantum Electrodynamics
321
15.1 Lagrangians, Interacting Fields
321
15.1.1 Nonlinear Lagrangians
321
15.1.2 Fermions in an External Field
322
15.1.3 Interaction of Electrons with the Radiation Field: Quantum Electrodynamics (QED)
322
15.2 The Interaction Representation, Perturbation Theory
323
15.2.1 The Interaction Representation (Dirac Representation)
324
15.2.2 Perturbation Theory
327
15.3 The S Matrix
328
15.3.1 General Formulation
328
15.3.2 Simple Transitions
332
15.4 Wick's Theorem
335
15.5 Simple Scattering Processes, Feynman Diagrams
339
15.5.1 The First-Order Term
339
15.5.2 Mott Scattering
341
15.5.3 Second-Order Processes
346
15.5.4 Feynman Rules of Quantum Electrodynamics
356
15.6 Radiative Corrections
358
15.6.1 The Self-Energy of the Electron
359
15.6.2 Self-Energy of the Photon, Vacuum Polarization
365
15.6.3 Vertex Corrections
366
15.6.4 The Ward Identity and Charge Renormalization
368
15.6.5 Anomalous Magnetic Moment of the Electron
371
Problems
373
Bibliography for Part III
375
Appendix 377
A Alternative Derivation of the Dirac Equation
377
B Dirac Matrices
379
B.1 Standard Representation
379
B.2 Chiral Representation
379
B.3 Majorana Representations
380
C Projection Operators for the Spin
380
C.1 Definition
380
C.2 Rest Frame
380
C.3 General Significance of the Projection Operator P(n)
381
D The Path-Integral Representation of Quantum Mechanics
385
E Covariant Quantization of the Electromagnetic Field, the Gupta–Bleuler Method
387
E.1 Quantization and the Feynman Propagator
387
E.2 The Physical Significance of Longitudinal and Scalar Photons
389
E.3 The Feynman Photon Propagator
392
E.4 Conserved Quantities
393
F Coupling of Charged Scalar Mesons to the Electromagnetic Field
394
Index 397