Author(s): J. Frenkel
Publisher: Mir Publishers
Year: 1950
Language: English
City: Moscow
Front Cover
Title PAge
PREFACE
CONTENTS
1. CLASSICAL MECHANICS AS THE LIMITING FORM OF WAVE MECHANICS
1. Motion in One Dimension; Par tial Reflection and Uncer tainty in the Sign of the Velocity
2. Compar ison between the Schr ddinger and the Classical Equation of Motion in One Dimension; Aver age Velocity and Current Density
3. Gener alization for Non-stationar y Motion in Thr ee Dimensions; The Hamilton-J acobi Equation
4. Compar ison of the Appr oximate Solutions of Schrödinger ’s Equation; Comparison of Classical and Wave-mechanical Aver age Values
5. Motion in a Limited Region; Quantum Conditions and Average Values
2. OPERATORS
6 . Operational Form of Schrödinger’s Equation, and Operational Representation of Physical Quantities
7. Characteristic Functions and Values of Operators; Oper ational Equations; Constants of the Motion
10. Orthogon a lity and Norm a lization of Characteristic Functions for Discrete and Continuous Spectra
3. MATRICES
11. Matrix Representation of Physical Quanties and Matrix Form of the Equation s of Motion
12. The Correspondene between Matrix and Classical Mechanics
13. Application of the Matrix Method to Oscillatory and Rotational Motion
14. Matrix Representation in the Case of a Continuous Spectrum
4. TRANSFORMATION THEORY
15. Restricted Transformation Theory; Matrices defined from different ‘Points of View’
16. Transformation of Matrices
17. Transformation Theory of Matrices as a Generalization of Wave Mechanics; Transformation of Basic Quantities
18. Geometrical Representation of the Transformation Theor y
5. PERTURBATION THEORY
19. Perturbation Theory not involving the Time (Method of Stationary States)
20. Extension of the Preceding Theory to the Case of ‘Relative Degener acy* and Continuous Spectr a; Effect of Perturbationon Various Physical Quantities
21. Perturbation Theory involving the Time; General Processes;Theory of Transitions
22. First Approximation; Theory of Simple Transitions
23. Second Approximation; Theory of Combined Transitions
24. Theory of Transitions for an Undefined Initial State
6. RELATIVISTIC REMODELLING AND MAGNETIC GENERALIZATION OF THE WAVE MECHANICS OF A SINGLE ELECTRON
25. Simplest Form of Relativistic Wave Mechanics
26. Magnetic Forces in the Approximate Non-Relativistic Wave Mechanics
27. Relativistic Wave Mechanics as a Formal Generalization of Maxwell’s Electromagetic Theory of Light
28. Alternative Form of the Wave Equations; Duplicity and Quadr uplicity Phenomenon
30. More Exact Form of the Two-dimensional Matrix Theory; Electron’s Electric Moment
31. The Exact Four-dimensional Matrix Theory of Dirac
33. The Motion of an Electron in a Central Field of Force; Fine Structure and Zeeman Effect
34. Negative Energy States; Positive Electrons and Neutr ons
35. The Invariance of the Dirac Equation with regard to Coordinate Transformations
36. Transformaion of the Dirac Equation to Curvilinear Coordinates
7. THE PROBLEM OF MANY PARTICLES
37. General Results, Virial Theorem, Linear and Angular Momentum
38. Magnetic For ces and Spin Effects
39. Complex Particles treated as Material Points with Inner Coordinates; Theory of Incomplete Systems
40. Identical Particles (Electrons) and the Exclusion Pr inciple
8. REDUCTION OF THE PROBLEM OF A SYSTEM OF IDENTICAL PARTICLES TO THAT OF A SINGLE PARTICLE
41. Perturbation Theory of a System of Spinless Electrons and the Exchange Degeneracy
42. Introduction of the Spin Coordinates and Solution of the Per tur bation Problem with Antisymmetrical Wave Functions
43. The Method of the Self-consistent Field with Factorized Wave Functions
44. The Method of the Self-consistent Field with Antisymmetrical Functions and Dirac’s Density Matrix
45. Approximate Solutions (Thomas-Fermi-Dirac Equation)
9. SECOND (INTENSITY) QUANTIZATION AND QUANTUM ELECTRODYNAMICS
46. Second Quantization with respect to Electrons
47. Intensity Quantization of Par ticles descr ibed in the Configuration Space by a Symmetrical Wave Function (Einstein -Bose Statistics)
48. Inter action between a ‘Doubly Quantized’ System and an Ordinary System: Application to Photons
49. Electr omagnetic Waves with Quantized Amplitudes; Theory of Spontaneous Transitions and of Radiation Damping
50. Application of Quantized Electron Waves to the Emission and Scattering of Radiation
51. Connexion between Quantized Mechanical (Electron) Waves and Electr omagnetic Waves
52. The Quantum Electrodynamics of Heisenberg, Pauli, and Dirac.
53. Breit’s Formula. Concluding Remarks
REFERENCES
INDEX TO PART I
INDEX TO PART II*
