Quantum Mechanics deals with various aspects of quantum mechanics and covers topics ranging from the uncertainty principle and the principle of superposition to conservation laws, Schrödinger's equation, and perturbation theory. Spin, radiation, and the identity of particles are also discussed, along with the atom, the diatomic molecule, elastic and inelastic collisions, and Feynman diagrams.
Comprised of 16 chapters, this volume begins with an overview of non-relativistic quantum theory and the basic concepts of quantum mechanics such as the principles of uncertainty and superposition, operators, and the density matrix. Subsequent chapters deal with conservation laws in quantum mechanics; Schrödinger's equation and general properties of its solutions; perturbations independent of time and dependent on time; spin and the spin operator; and the principle of indistinguishability of similar particles. The atom and its electron states are also examined, together with diatomic molecules; elastic and inelastic collisions; photons and electrons; Dirac's equation; and particles and antiparticles. The final chapter is devoted to Feynman diagrams, paying particular attention to the scattering matrix, radiative corrections, and radiative shift of atomic levels.
This book will be of interest to physicists.
Inhaltsverzeichnis
1;Front Cover;1 2;Quantum Mechanics;4 3;Copyright Page;5 4;Table of Contents;6 5;PREFACE;10 6;PUBLISHER'S NOTE;11 7;NOTATION;12 8;Part I: Non-relativistic theory;14 8.1;CHAPTER 1. THE BASIC CONCEPTS OF QUANTUM MECHANICS;16 8.1.1;1. The uncertainty principle;16 8.1.2;2. The principle of superposition;22 8.1.3;3. Operators;25 8.1.4;4. Addition and multiplication of operators;31 8.1.5;5. The continuous spectrum;34 8.1.6;6. The passage to the limiting case of classical mechanics;37 8.1.7;7. The density matrix;39 8.2;CHAPTER 2. CONSERVATION LAWS IN QUANTUM MECHANICS;41 8.2.1;8. The Hamiltonian operator;41 8.2.2;9. The differentiation of operators with respect to time;42 8.2.3;10. Stationary states;44 8.2.4;11. Matrices of physical quantities;47 8.2.5;12. Momentum;51 8.2.6;13. Uncertainty relations;55 8.2.7;14. Angular momentum;57 8.2.8;15. Eigenvalues of the angular momentum;62 8.2.9;16. Eigenfunctions of the angular momentum;66 8.2.10;17. Addition of angular momenta;68 8.2.11;18. Angular momentum selection rules;71 8.2.12;19. Parity of a state;75 8.3;CHAPTER 3. SCHRÖDINGER'S EQUATION;80 8.3.1;20. Schrödinger's equation;80 8.3.2;21. The current density;82 8.3.3;22. General properties of solutions of Schrödinger's equation;85 8.3.4;23. Time reversal;89 8.3.5;24. The potential well;90 8.3.6;25. The linear oscillator;94 8.3.7;26. The quasi-classical wave function;99 8.3.8;27. Bohr and Sommerfeld's quantisation rule;102 8.3.9;28. The transmission coefficient;108 8.3.10;29. Motion in a centrally symmetric field;114 8.3.11;30. Spherical waves;118 8.3.12;31. Motion in a Coulomb field;123 8.4;CHAPTER 4. PERTURBATION THEORY;129 8.4.1;32. Perturbations independent of time;129 8.4.2;33. The secular equation;134 8.4.3;34. Perturbations depending on time;136 8.4.4;35. Transitions in the continuous spectrum;139 8.4.5;36. Intermediate states;142 8.4.6;37. The uncertainty relation for energy;143 8.4.7;38. Quasi-stationary states;146 8.5;CHAPTER 5. SPIN;149 8.5.1;39. Spin;149 8.5.2;40. T
he spin operator;152 8.5.3;41. Spinors;154 8.5.4;42. Polarisation of electrons;159 8.5.5;43. A particle in a magnetic field;162 8.5.6;44. Motion in a uniform magnetic field;164 8.6;CHAPTER 6. IDENTITY OF PARTICLES;167 8.6.1;45. The principle of indistinguishability of similar particles;167 8.6.2;46. Exchange interaction;171 8.6.3;47. Second quantisation. The case of Bose statistics;174 8.6.4;48. Second quantisation. The case of Fermi statistics;180 8.7;CHAPTER 7. THE ATOM;182 8.7.1;49. Atomic energy levels;182 8.7.2;50. Electron states in the atom;184 8.7.3;51. Fine structure of atomic levels;187 8.7.4;52. The Mendeleev periodic system;191 8.7.5;53. X-ray terms;197 8.7.6;54. An atom in an electric field;200 8.7.7;55. An atom in a magnetic field;205 8.8;CHAPTER 8. THE DIATOMIC MOLECULE;210 8.8.1;56. Electron terms in the diatomic molecule;210 8.8.2;57. The intersection of electron terms;212 8.8.3;58. Valency;215 8.8.4;59. Vibrational and rotational structures of terms in the diatomic molecule;222 8.8.5;60. Parahydrogen and orthohydrogen;226 8.8.6;61. Van der Waals forces;228 8.9;CHAPTER 9. ELASTIC COLLISIONS;231 8.9.1;62. The scattering amplitude;231 8.9.2;63. The condition for quasi-classical scattering;234 8.9.3;64. Discrete energy levels as poles of the scattering amplitude;236 8.9.4;65. The scattering of slow particles;238 8.9.5;66. Resonance scattering at low energies;241 8.9.6;67. Born's formula;243 8.9.7;68. Rutherford's formula;250 8.9.8;69. Collisions of like particles;252 8.9.9;70. Elastic collisions between fast electrons and atoms;254 8.10;CHAPTER 10. INELASTIC COLLISIONS;259 8.10.1;71. The principle of detailed balancing;259 8.10.2;72. Elastic scattering in the presence of inelastic processes;263 8.10.3;73. Inelastic scattering of slow particles;265 8.10.4;74. Inelastic collisions between fast particles and atoms;266 9;Part II: Relativistic theory;270 9.1;CHAPTER 11. PHOTONS;272 9.1.1;75. The uncertainty principle in the relativistic case;272 9.1.2;76. Q
uantisation of the free electromagnetic field;277 9.1.3;77. Photons;281 9.1.4;78. The angular momentum and parity of the photon;284 9.2;CHAPTER 12. DIRAC'S EQUATION;288 9.2.1;79. The KleinFock equation;288 9.2.2;80. Four-dimensional spinors;290 9.2.3;81. Inversion of spinors;294 9.2.4;82. Dirac's equation;296 9.2.5;83. Dirac matrices;299 9.2.6;84. The current density in Dirac's equation;302 9.3;CHAPTER 13. PARTICLES AND ANTIPARTICLES;306 9.3.1;85. .-operators;306 9.3.2;86. Particles and antiparticles;309 9.3.3;87. The relation between the spin and the statistics;313 9.3.4;88. Strictly neutral particles;314 9.3.5;89. Internal parity of particles;317 9.3.6;90. The CPT theorem;320 9.3.7;91. Neutrinos;324 9.4;CHAPTER 14. ELECTRONS IN AN EXTERNAL FIELD;327 9.4.1;92. Dirac's equation for an electron in an external field;327 9.4.2;93. Magnetic moment of the electron;328 9.4.3;94. Spinorbit interaction;332 9.5;CHAPTER 15. RADIATION;335 9.5.1;95. The electromagnetic interaction operator;335 9.5.2;96. Spontaneous and stimulated emission;339 9.5.3;97. Dipole radiation;342 9.5.4;98. Multipole radiation;344 9.5.5;99. Radiation from atoms;346 9.5.6;100. The infra-red catastrophe;348 9.5.7;101. Scattering of radiation;351 9.5.8;102. Natural width of spectral lines;356 9.6;CHAPTER 16. FEYNMAN DIAGRAMS;358 9.6.1;103. The scattering matrix;358 9.6.2;104. Feynman diagrams;363 9.6.3;105. Radiative corrections;371 9.6.4;106. Radiative shift of atomic levels;373 10;INDEX;376
