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Advanced Quantum Mechanics Fourth Edition 2008 [Minkštas viršelis]

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  • Formatas: Paperback / softback, 405 pages, aukštis x plotis: 235x155 mm, weight: 1325 g, XVII, 405 p., 1 Paperback / softback
  • Išleidimo metai: 19-Oct-2010
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642098746
  • ISBN-13: 9783642098741
Kitos knygos pagal šią temą:
Advanced Quantum Mechanics Fourth Edition 2008Didesnis paveikslėlis
  • Formatas: Paperback / softback, 405 pages, aukštis x plotis: 235x155 mm, weight: 1325 g, XVII, 405 p., 1 Paperback / softback
  • Išleidimo metai: 19-Oct-2010
  • Leidėjas: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642098746
  • ISBN-13: 9783642098741
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9783642098741.html
Raktažodžiai:
This, the second volume on quantum mechanics by Franz Schwabl, discusses nonrelativistic multi-particle systems, relativistic wave equations and relativistic quantum fields. Numerous exercises help the reader gain a thorough working knowledge of the subject.

Characteristic of Schwabl's work, this volume features a compelling mathematical presentation in which all intermediate steps are derived and where numerous examples for application and exercises help the reader to gain a thorough working knowledge of the subject. The treatment of relativistic wave equations and their symmetries and the fundamentals of quantum field theory lay the foundations for advanced studies in solid-state physics, nuclear and elementary particle physics. New material has been added to this third edition.

This, the second volume on quantum mechanics by Franz Schwabl, discusses nonrelativistic multi-particle systems, relativistic wave equations and relativistic quantum fields. Numerous exercises help the reader gain a thorough working knowledge of the subject.

Daugiau informacijos

4th edition
Part I Nonrelativistic Many-Particle Systems
1 Second Quantization
3(30)
1.1 Identical Particles, Many-Particle States, and Permutation Symmetry
3(5)
1.1.1 States and Observables of Identical Particles
3(3)
1.1.2 Examples
6(2)
1.2 Completely Symmetric and Antisymmetric States
8(2)
1.3 Bosons
10(6)
1.3.1 States, Fock Space, Creation and Annihilation Operators
10(3)
1.3.2 The Particle-Number Operator
13(1)
1.3.3 General Single- and Many-Particle Operators
14(2)
1.4 Fermions
16(4)
1.4.1 States, Fock Space, Creation and Annihilation Operators
16(3)
1.4.2 Single- and Many-Particle Operators
19(1)
1.5 Field Operators
20(5)
1.5.1 Transformations Between Different Basis Systems
20(1)
1.5.2 Field Operators
21(2)
1.5.3 Field Equations
23(2)
1.6 Momentum Representation
25(8)
1.6.1 Momentum Eigenfunctions and the Hamiltonian
25(2)
1.6.2 Fourier Transformation of the Density
27(1)
1.6.3 The Inclusion of Spin
27(2)
Problems
29(4)
2 Spin-1/2 Fermions
33(22)
2.1 Noninteracting Fermions
33(8)
2.1.1 The Fermi Sphere, Excitations
33(2)
2.1.2 Single-Particle Correlation Function
35(1)
2.1.3 Pair Distribution Function
36(3)
2.1.4 Pair Distribution Function, Density Correlation Functions, and Structure Factor
39(2)
2.2 Ground State Energy and Elementary Theory of the Electron Gas
41(8)
2.2.1 Hamiltonian
41(1)
2.2.2 Ground State Energy in the Hartree-Fock Approximation
42(4)
2.2.3 Modification of Electron Energy Levels due to the Coulomb Interaction
46(3)
2.3 Hartree-Fock Equations for Atoms
49(6)
Problems
52(3)
3 Bosons
55(20)
3.1 Free Bosons
55(5)
3.1.1 Pair Distribution Function for Free Bosons
55(2)
3.1.2 Two-Particle States of Bosons
57(3)
3.2 Weakly Interacting, Dilute Bose Gas
60(15)
3.2.1 Quantum Fluids and Bose-Einstein Condensation
60(2)
3.2.2 Bogoliubov Theory of the Weakly Interacting Bose Gas
62(7)
3.2.3 Superfluidity
69(3)
Problems
72(3)
4 Correlation Functions, Scattering, and Response
75(40)
4.1 Scattering and Response
75(7)
4.2 Density Matrix, Correlation Functions
82(3)
4.3 Dynamical Susceptibility
85(4)
4.4 Dispersion Relations
89(1)
4.5 Spectral Representation
90(1)
4.6 Fluctuation-Dissipation Theorem
91(2)
4.7 Examples of Applications
93(7)
4.8 Symmetry Properties
100(7)
4.8.1 General Symmetry Relations
100(2)
4.8.2 Symmetry Properties of the Response Function for Hermitian Operators
102(5)
4.9 Sum Rules
107(8)
4.9.1 General Structure of Sum Rules
107(1)
4.9.2 Application to the Excitations in He II
108(1)
Problems
109(2)
Bibliography for Part I
111(4)
Part II Relativistic Wave Equations
5 Relativistic Wave Equations and their Derivation
115(16)
5.1 Introduction
115(1)
5.2 The Klein-Gordon Equation
116(4)
5.2.1 Derivation by Means of the Correspondence Principle
116(3)
5.2.2 The Continuity Equation
119(1)
5.2.3 Free Solutions of the Klein-Gordon Equation
120(1)
5.3 Dirac Equation
120(11)
5.3.1 Derivation of the Dirac Equation
120(2)
5.3.2 The Continuity Equation
122(1)
5.3.3 Properties of the Dirac Matrices
123(1)
5.3.4 The Dirac Equation in Covariant Form
123(2)
5.3.5 Nonrelativistic Limit and Coupling to the Electromagnetic Field
125(5)
Problems
130(1)
6 Lorentz Transformations and Covariance of the Dirac Equation
131(24)
6.1 Lorentz Transformations
131(4)
6.2 Lorentz Covariance of the Dirac Equation
135(11)
6.2.1 Lorentz Covariance and Transformation of Spinors
135(1)
6.2.2 Determination of the Representation S(Λ)
136(6)
6.2.3 Further Properties of S
142(2)
6.2.4 Transformation of Bilinear Forms
144(1)
6.2.5 Properties of the γ Matrices
145(1)
6.3 Solutions of the Dirac Equation for Free Particles
146(9)
6.3.1 Spinors with Finite Momentum
146(3)
6.3.2 Orthogonality Relations and Density
149(2)
6.3.3 Projection Operators
151(1)
Problems
152(3)
7 Orbital Angular Momentum and Spin
155(6)
7.1 Passive and Active Transformations
155(1)
7.2 Rotations and Angular Momentum
156(5)
Problems
159(2)
8 The Coulomb Potential
161(20)
8.1 Klein-Gordon Equation with Electromagnetic Field
161(7)
8.1.1 Coupling to the Electromagnetic Field
161(1)
8.1.2 Klein-Gordon Equation in a Coulomb Field
162(6)
8.2 Dirac Equation for the Coulomb Potential
168(13)
Problems
180(1)
9 The Foldy-Wouthuysen Transformation and Relativistic Corrections
181(14)
9.1 The Foldy-Wouthuysen Transformation
181(6)
9.1.1 Description of the Problem
181(1)
9.1.2 Transformation for Free Particles
182(1)
9.1.3 Interaction with the Electromagnetic Field
183(4)
9.2 Relativistic Corrections and the Lamb Shift
187(8)
9.2.1 Relativistic Corrections
187(2)
9.2.2 Estimate of the Lamb Shift
189(4)
Problems
193(2)
10 Physical Interpretation of the Solutions to the Dirac Equation
195(14)
10.1 Wave Packets and "Zitterbewegung"
195(9)
10.1.1 Superposition of Positive Energy States
196(1)
10.1.2 The General Wave Packet
197(3)
10.1.3 General Solution of the Free Dirac Equation in the Heisenberg Representation
200(2)
10.1.4 Potential Steps and the Klein Paradox
202(2)
10.2 The Hole Theory
204(5)
Problems
207(2)
11 Symmetries and Further Properties of the Dirac Equation
209(40)
11.1 Active and Passive Transformations, Transformations of Vectors
209(3)
11.2 Invariance and Conservation Laws
212(2)
11.2.1 The General Transformation
212(1)
11.2.2 Rotations
212(1)
11.2.3 Translations
213(1)
11.2.4 Spatial Reflection (Parity Transformation)
213(1)
11.3 Charge Conjugation
214(3)
11.4 Time Reversal (Motion Reversal)
217(19)
11.4.1 Reversal of Motion in Classical Physics
218(3)
11.4.2 Time Reversal in Quantum Mechanics
221(8)
11.4.3 Time-Reversal Invariance of the Dirac Equation
229(6)
11.4.4 Racah Time Reflection
235(1)
11.5 Helicity
236(3)
11.6 Zero-Mass Fermions (Neutrinos)
239(10)
Problems
244(1)
Bibliography for Part II
245(4)
Part III Relativistic Fields
12 Quantization of Relativistic Fields
249(28)
12.1 Coupled Oscillators, the Linear Chain, Lattice Vibrations
249(12)
12.1.1 Linear Chain of Coupled Oscillators
249(6)
12.1.2 Continuum Limit, Vibrating String
255(3)
12.1.3 Generalization to Three Dimensions, Relationship to the Klein-Gordon Field
258(3)
12.2 Classical Field Theory
261(5)
12.2.1 Lagrangian and Euler-Lagrange Equations of Motion
261(5)
12.3 Canonical Quantization
266(1)
12.4 Symmetries and Conservation Laws, Noether's Theorem
266(11)
12.4.1 The Energy-Momentum Tensor, Continuity Equations, and Conservation Laws
266(2)
12.4.2 Derivation from Noether's Theorem of the Conservation Laws for Four-Momentum, Angular Momentum, and Charge
268(7)
Problems
275(2)
13 Free Fields
277(30)
13.1 The Real Klein-Gordon Field
277(8)
13.1.1 The Lagrangian Density, Commutation Relations, and the Hamiltonian
277(4)
13.1.2 Propagators
281(4)
13.2 The Complex Klein-Gordon Field
285(2)
13.3 Quantization of the Dirac Field
287(9)
13.3.1 Field Equations
287(2)
13.3.2 Conserved Quantities
289(1)
13.3.3 Quantization
290(3)
13.3.4 Charge
293(2)
13.3.5 The Infinite-Volume Limit
295(1)
13.4 The Spin Statistics Theorem
296(11)
13.4.1 Propagators and the Spin Statistics Theorem
296(5)
13.4.2 Further Properties of Anticommutators and Propagators of the Dirac Field
301(2)
Problems
303(4)
14 Quantization of the Radiation Field
307(14)
14.1 Classical Electrodynamics
307(2)
14.1.1 Maxwell Equations
307(2)
14.1.2 Gauge Transformations
309(1)
14.2 The Coulomb Gauge
309(2)
14.3 The Lagrangian Density for the Electromagnetic Field
311(1)
14.4 The Free Electromagnatic Field and its Quantization
312(4)
14.5 Calculation of the Photon Propagator
316(5)
Problems
320(1)
15 Interacting Fields, Quantum Electrodynamics
321(56)
15.1 Lagrangians, Interacting Fields
321(2)
15.1.1 Nonlinear Lagrangians
321(1)
15.1.2 Fermions in an External Field
322(1)
15.1.3 Interaction of Electrons with the Radiation Field: Quantum Electrodynamics (QED)
322(1)
15.2 The Interaction Representation, Perturbation Theory
323(5)
15.2.1 The Interaction Representation (Dirac Representation)
324(3)
15.2.2 Perturbation Theory
327(1)
15.3 The S Matrix
328(7)
15.3.1 General Formulation
328(4)
15.3.2 Simple Transitions
332(3)
15.4 Wick's Theorem
335(4)
15.5 Simple Scattering Processes, Feynman Diagrams
339(19)
15.5.1 The First-Order Term
339(2)
15.5.2 Mott Scattering
341(5)
15.5.3 Second-Order Processes
346(10)
15.5.4 Feynman Rules of Quantum Electrodynamics
356(2)
15.6 Radiative Corrections
358(19)
15.6.1 The Self-Energy of the Electron
359(6)
15.6.2 Self-Energy of the Photon, Vacuum Polarization
365(1)
15.6.3 Vertex Corrections
366(2)
15.6.4 The Ward Identity and Charge Renormalization
368(3)
15.6.5 Anomalous Magnetic Moment of the Electron
371(2)
Problems
373(2)
Bibliography for Part III
375(2)
Appendix
377(20)
A Alternative Derivation of the Dirac Equation
377(2)
B Dirac Matrices
379(1)
B.1 Standard Representation
379(1)
B.2 Chiral Representation
379(1)
B.3 Majorana Representations
380(1)
C Projection Operators for the Spin
380(5)
C.1 Definition
380(1)
C.2 Rest Frame
380(1)
C.3 General Significance of the Projection Operator P(n)
381(4)
D The Path-Integral Representation of Quantum Mechanics
385(2)
E Covariant Quantization of the Electromagnetic Field, the Gupta-Bleuler Method
387(7)
E.1 Quantization and the Feynman Propagator
387(2)
E.2 The Physical Significance of Longitudinal and Scalar Photons
389(3)
E.3 The Feynman Photon Propagator
392(1)
E.4 Conserved Quantities
393(1)
F Coupling of Charged Scalar Mesons to the Electromagnetic Field
394(3)
Index 397