Fundamentals of Theoretical Physics: Volume 2 - Quantum Mechanics

Description

Front Cover Title Page PREFACE CONTENTS 1 FOUNDATIONS OF QUANTUM MECHANICS 1. lntrodudion 2. State 3. The Superposition Principle 4. The Physical Meaning of the Psi-Function 5. The Schrodinger Equation 6. Probability Flux Density 2 MATHEMATICAL TOOLS OF QUANTUM MECHANICS 7. Fundamental Postulates 8. Linear Operators 9. Matrix Representation of Operators 10. The Algebra of Operators 11. The Uncertainty Relation 12. The Continuous Spectrum 13. Dirac Notation 14. Transformation of Functions and Operators from One Representation to Another 3 EIGENVALUES AND EIGENFUNCTIONS OF PHYSICAL QUANTITIES 15. Operators of Physical Quantities 16. Rules for Commutation of Operators of Physical Quantities 17. Eigenfunctions of the Coordinate and Momentum Operators 18. Momentum and Energy Representations 19. Eigenvalues and Eigenfunctions of the Angular Momentum Operator 20. Parity 4 TIME DEPENDENCE OF PHYSICAL QUANTITIES 21. The Time Derivative of an Operator 22. Time Dependence of Matrix Elements 5 MOTION OF A PARTICLE IN FORCE FIELDS 23. A Particle in a Central Force Field 24. An Electron in a Coulomb Field. The Hydrogen Atom 25. The Harmonic Oscillator 26. Solution of the Harmonic Oscillator Problem in the Matrix Form 27. Annihilation and Creation Operators 6 PERTURBATION THEORY 28. Introduction 29. Time-Independent Perturbations 30. Case of Two Close Levels 31. Degenerate Case 32. Examples of Application of the Stationary Perturbation Theory 33. Time-Dependent Perturbations 34. Perturbations Varying Harmonically with Time 35. Transitions in a Continuous Spectrum 36. Potential Energy as a Perturbation 7 THE OUASICLASSICAL APPROXIMATION: 37. The Classical Limit 38. Boundary Conditions at a Turning Point 39. Bohr-Sommerfeld Quantization Rule 40. Penetration of a Potential Barrier 8 SEMIEMPIRICAL THEORY OF PARTICLES WITH SPIN 41. Psi-Function of a Particle with Spin 42. Spin Operators 43. Eigenvalues and Eigenfunctions of Spin Operators 44. Spinors 9 SYSTEMS CONSISTING OF IDENTICAL PARTICLES 45. Principle of Indistinguishability of Identical Particles 46. Psi-Functions for Systems of Particles. The Pauli Principle 47. Summation of Angular Momenta 48. Psi-Function of System of Two Particles Having a Spin of 1/2 49. Exchange Interaction 50. Second Quantization 51. Second Quantization Applied to Bosons 52. Second Quantization Applied to Fermions 10 ATOMS A.HD MOLECULES 53. Methods of Calculating Atomic Systems 54. The Helium Atom 55. The Variation Method 56. The. Method of the Self~Consistent Field 57. The Thomas-Fermi Method 58. The Zeeman Effect 59. The Theory of Molecules in the Adiabatic Approximation 60. The Hydrogen Molecule 11 RADIATION THEORY 61. Quantization of an Electromagnetic Field 62. Interaction of an Electromagnetic Field with a Charged Particle 63. One-Photon Processes 64. Dipole Radiation 65. Selectlon Rules 12 SCATTERING THEORY 66. Scattering Cross Section 67. Statfering Amplitude 68. Born Approximation 69. Method of Partial Waves 70. Inelastic Scattering APPENDICES I. Angular Momentum Operators in Spherical Coordinates II. Spherical Functions III. Chebyshev-Hermite Polynomials IV. Some Information from the Theory of Functions of a Complex Variable V. Airy Function VI. Method of Green's Functions VII. Solution of the Fundamental Equation of the Scattering Theory by the Method of Green's Functions VIII. The Dirac Delta Function INDEX