Greiner Relativistic Quantum Mechanics

Wave Equations
Erscheinungsjahr 2012
ISBN: 978-3-642-88082-7
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 345 Seiten, eBook

More than a generation of Gennan-speaking students around the world have worked their way to an understanding and appreciation of the power and beauty of modern theoretical physics - with mathematics, the most fundamental of sciences - using Walter Greiner's textbooks as their guide. The idea of developing a coherent, complete presentation of an entire field of science in a series of closely related textbooks is not a new one. Many older physicists remember with real pleasure their sense of adventure and discovery as they worked their ways through the classic series by Sommerfeld, by Planck and by Landau and Lifshitz. From the students' viewpoint, there are a great many obvious advantages to be gained through use of consistent notation, logical ordering of topics and coherence of presentation; beyond this, the complete coverage of the science provides a unique opportunity for the author to convey his personal enthusiasm and love for his subject. The present five volume set, Theoretical Physics, is in fact only that part of the complete set of textbooks developed by Greiner and his students that presents the quantum theory. I have long urged him to make the remaining volumes on classical mechanics and dynamics, on electromagnetism, on nuclear and particle physics, and on special topics available to an English-speaking audience as well, and we can hope for these companion volumes covering all of theoretical physics some time in the future.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Greiner, Walter

Inhaltsverzeichnis

1. Relativistic Wave Equation for Spin-0 Particles The Klein-Gordon Equation and Its Applications.- 1.1 The Notation.- 1.2 The Klein-Gordon Equation.- 1.3 The Nonrelativistic Limit.- 1.4 Free Spin-0 Particles.- 1.5 Energy-Momentum Tensor of the Klein-Gordon Field.- 1.6 The Klein-Gordon Equation in Schrödinger Form.- 1.7 Charge Conjugation.- 1.8 Free Spin-0 Particles in the Feshbach-Villars Representation.- 1.9 The Interaction of a Spin-0 Particle with an Electromagnetic Field.- 1.10 Gauge In variance of the Coupling.- 1.11 The Nonrelativistic Limit With Fields.- 1.12 Interpretation of One-Particle Operators in Relativistic Quantum Mechanics.- Biographical Notes.- 2. A Wave Equation for Spin-$$\frac{1}{2}$$ Particles — The Dirac Equation.- 2.1 Free Motion of a Dirac Particle.- 2.2 Single-Particle Interpretation of the Plane (Free) Dirac Waves.- 2.3 Nonrelativistic Limit of the Dirac Equation.- Biographical Notes.- 3. Lorentz-Covariance of the Dirac Equation.- 3.1 Formulation of Covariance (Form Invariance).- 3.2 Construction of the ? Operator for Infinitesimal Lorentz Transformations.- 3.3 Finite Proper Lorentz Transformations.- 3.4 The ? Operator for Proper Lorentz Transformations.- 3.5 The Four-Current Density.- Biographical Notes.- 4. Spinors under Spatial Reflection.- 5. Bilinear Covariants of the Dirac Spinors.- Biographical Notes.- 6. Another Way of Constructing Solutions of the Free Dirac Equation: Construction by Lorentz Transformations.- 6.1 Plane Waves in Arbitrary Directions.- 6.2 The General Form of the Free Solutions and Their Properties.- 6.3 Polarized Electrons in Relativistic Theory.- 7. Projection Operators for Energy and Spin.- 7.1 Simultaneous Projections of Energy and Spin.- 8. Wave Packets of Plane Dirac Waves.- 9. Dirac Particles in ExternalFields: Examples and Problems.- 10. The Two-Centre Dirac Equation.- 11. The Foldy-Wouthuysen Representation for Free Particles.- 11.1 The Foldy-Wouthuysen Representation in the Presence of External Fields.- 12. The Hole Theory.- 12.1 Charge Conjugation.- 12.2 Charge Conjugation of Eigenstates with Arbitrary Spin and Momentum.- 12.3 Charge Conjugation of Bound States.- 12.4 Time Reversal and PCT Symmetry.- Biographical Notes.- 13. Klein’s Paradox.- 14. The Weyl Equation — The Neutrino.- 15. Wave Equations for Particles with Arbitrary Spins.- 15.1 Particles with Finite Mass.- 15.2 Massless Particles.- 15.3 Spin-1 Fields for Particles with Finite Mass; Proca Equations.- 15.4 Kemmer Equation.- 15.5 The Maxwell Equations.- 15.6 Spin-$$\frac{3}{2}$$ Fields.- Biographical Notes.- 16. Lorentz Invariance and Relativistic Symmetry Principles.- 16.1 Orthogonal Transformations in Four Dimensions.- 16.2 Infinitesimal Transformations and the Proper Subgroup of O(4).- 16.3 Classification of the Subgroups of O(4).- 16.4 The Inhomogeneous Lorentz Group.- 16.5 The Conformal Group.- 16.6 Representations of the Four-Dimensional Orthogonal Group and Its Subgroups.- 16.7 Representation of SL(2,C).- 16.8 Representations of SO(3,R).- 16.9 Representations of the Lorentz Group Lp.- 16.10 Spin and the Rotation Group.- Biographical Notes.