Quantum Mechanics (eBook)

International Series in Natural Philosophy

A. S. Davydov (Autor)

D. ter Haar (Herausgeber)

eBook Download: PDF

2013 | 2. Auflage
652 Seiten
Elsevier Science (Verlag)
978-1-4831-8783-9 (ISBN)

Infos

Quantum Mechanics, Second Edition discusses the fundamental concepts and governing principles of quantum mechanics. The title details the physical ideas and the mathematical formalism of the quantum theory of the non-relativistic and quasi-relativistic motion of a single particle in an external field. The text first covers the basic concepts, and then proceeds to tackling the change of quantum states in time. Next, the selection examines the connection between quantum mechanics and classical mechanics. The book also discusses the simplest applications of quantum mechanics, along with the elementary representation theory. The book will be most useful to students of physics who are studying quantum mechanics. The text will also serve expert quantum physicists as a reference.

Inhalt

Front Cover 1
Quantum Mechanics 4
Copyright Page 5
Table of Contents 6
PREFACE 12
PREFACE TO SECOND EDITION 13
PREFACE TO THE ENGLISH EDITION 14
CHAPTER I. THE BASIC CONCEPTS OF QUANTUM MECHANICS 16
1. Introduction 16
2. The wavefunction of a free particle 19
3. The principle of superposition of states: wavepackets 21
4. Statistical interpretation of the wavefunction 24
5. Free particle in a bounded volume in space 26
6. Calculation of the average values of the coordinate and the momentum 27
7. Operators corresponding to physical quantities 29
8. Eigenfunctions and eigenvalues of operators 34
9. Properties of the eigenfunctions of operators with a discrete spectrum 39
10. Properties of the eigenfunctions of operators with a continuous spectrum 42
11. The conditions under which several physical quantities can have well-defined values in the same state 46
12. Methods to determine the states of quantum systems 48
13. The Heisenberg relations for physical quantities 51
14. Description of states by means of the density matrix 56
Problems 61
CHAPTER II. CHANGE OF QUANTUM STATES IN TIME 63
15. The Schrödinger wave equation 63
16. Stationary states 66
17. Change in time of average values of physical quantities 70
18. Integrals of motion and symmetry conditions 73
19. Group theory in quantum mechanics 80
20. Change with time of states described by a density matrix 83
Problems 85
CHAPTER III. THE CONNEXION BETWEEN QUANTUM MECHANICS AND CLASSICAL MECHANICS 86
21. The limiting transition from quantum to classical mechanics 86
22. Semi-classical approximation 88
23*. The Bohr-Sommerfeld quantisation rules 91
24. Passage through a potential barrier: motion of a particle over a potential barrier or over a potential well 95
Problems 101
CHAPTER IV. THE SIMPLEST APPLICATIONS OF QUANTUM MECHANICS 102
25. A particle in a rectangular potential well 102
26. The harmonic oscillator 112
Problems 117
CHAPTER V. ELEMENTARY REPRESENTATION THEORY 118
27. Different representations of the state vector 118
28. Different representations of operators 123
29. The determination of the eigenfunctions and eigenvalues of operators given in the form of matrices 130
30. The general theory of unitary transformations 132
31. Unitary transformations corresponding to a change of state with time 136
32. Occupation number representation for the harmonic oscillator 141
33. The occupation number representation for the vibrations of atoms in a one-dimensional crystal 150
Problems 154
CHAPTER VI. THE MOTION OF APARTICLE IN ACENTRAL FIELD OF FORCE 155
34. General properties of the motion of a particle in a spherically symmetric field 155
35. Free motion with a well-defined value of the orbital angular momentum 157
36. Motion in a spherically symmetric rectangular potential well 160
37. Spherically symmetric oscillator well 163
38. Motion in a Coulomb field the discrete spectrum
39. Motion in a Coulomb field the continuous spectrum
40*. Angular momentum operator 173
41. Vector addition of two angular momenta 176
42. Vector addition of three angular momenta Racah coefficients
43. Transformation of the eigenfunctions of the angular momentum operators under a rotation of the coordinate axes 182
44. The generalised spherical functions as eigenfunctions of the angular momentum operator 188
45. Rotation of a rigid body the symmetrical top
46. Rotation of a rigid body the asymmetrical top
Problems 198
CHAPTER VII. APPROXIMATE METHODS FOR EVALUATING EIGENVALUES AND EIGENFUNCTIONS 200
47. Perturbation theory for stationary discrete states of a spectrum 200
48. Conditions for the applicability of perturbation theory 203
49. Perturbation theory when two levels are close 206
50. Perturbation theory for degenerate levels 208
51. Applications of the variational method to approximate calculations 209
52. The method of canonical transformations 214
Problems 219
CHAPTER VIII. THE FOUNDATIONS OF AQUASI-RELATIVISTIC QUANTUM THEORY OF THE MOTION OF APARTICLE IN AN EXTERNAL FIELD 222
53. Elementary particles in quantum mechanics 222
54. Relativistic equation for a zero-spin particle 224
55. Free spin-zero particles 228
56. Free zero-spin particles in the Feshbach-Villars representation 234
57. Integrals of motion and eigenvalues of operators in a relativistic theory of a zero-spin particle 236
58. Interaction of a spin-zero particle with an electromagnetic field 241
59. Dirac's relativistic equation 247
60. Free motion of particles described by the Dirac equation 251
61. Covariant form of the Dirac equation 258
62. The angular momentum of the electron in the Dirac theory 268
63. Relativistic corrections to the motion of an electron in an electromagnetic field 272
64. Spin-orbit interaction 275
65. Charge conjugation particles and antiparticles
66. The Dirac equation for a zero-rest-mass particle. the neutrino 285
67. The hydrogen atom, taking the electron spin into account 288
68. Exact solution of the Dirac equation for a Coulomb field 294
69. Atom in an external magnetic field 298
70. Atom in an external electric field 303
Problems 306
CHAPTER IX. QUANTUM THEORY OF SYSTEMS CONSISTING OF IDENTICAL PARTICLES 308
71. The Schrodinger equation for a system consisting of identical particles 308
72. Symmetric and antisymmetric wavefunctions 310
73. Elementary theory of the ground state of two-electron atoms 316
74. Excited states of the helium atom ortho- and para-helium
75. Self-consistent Hartree-Fock field 323
76. The statistical Thomas-Fermi method 329
77. The periodic system 333
78. Spectral and X-ray terms 336
79. The shell model of the atomic nucleus 341
Problems 345
CHAPTER X. SECOND QUANTISATION OF SYSTEMS OF IDENTICAL BOSONS 347
80. Second quantisation of the electromagnetic field without charges 347
81. Photons with a well-defined angular momentum and parity 352
82. Phonons in a three-dimensional crystal 358
83. Second quantisation of the meson field 362
84. Quasi-particles in a system of interacting bosons 365
85. Basic ideas of a microscopic theory of superfluidity 371
Problems 376
CHAPTER XI. SECOND QUANTISATION OF SYSTEMS OF IDENTICAL FERMIONS 377
86. Occupation number representation for systems of non-interacting fermions 377
87*. Systems of' fermions interacting through pair forces Bogolyubov's canonical transformation
88. The interaction of electrons with the phonons in a metal and the microscopic theory of superconductivity 392
89. Quantisation of the electron-positron field 397
Problems 400
CHAPTER XII. THE THEORY OF QUANTUM TRANSITIONS UNDER THE INFLUENCE OF AN EXTERNAL PERTURBATION 403
90. A general expression for the probability of a transition from one state to another 403
91. Excitation of an atom through bombardment by a heavy particle 407
92. Adiabatic and sudden switching on and switching off of the interaction 409
93. Transition probability per unit time 414
94. The interaction of a quantum system with electromagnetic radiation 416
95. Selection rules for the emission and absorption of light multipole radiation
96. Lifetime of excited states and width of energy levels 428
97. Linear response of a quantum system to an external agent 431
98. Polarisability of a quantum system 436
99. Elementary theory of the photoeffect 441
100. Transitions caused by time-independent interactions 443
101. Probability for quantum transitions and the– matrix 446
Problems 449
CHAPTER XIII. QUANTUM THEORY OF RELAXATION PROCESSES 450
102. The statistical operator of a dynamical subsystem 450
103. The simplest model of a quantum system interacting with a thermostat 453
104. The probability for the transfer of excitation energy from a donor to an acceptor when a dissipative medium is present 456
105. The fluctuation-dissipation theorem for the generalised susceptibility 462
Problems 464
CHAPTER XIV. QUANTUM THEORY OF SCATTERING 466
106. Elastic scattering of spin-zero particles 466
107. The free particle Green function 472
108. Theory of elastic scattering in the Born approximation 475
109. Partial wave method in scattering theory 477
110. Elastic scattering of slow particles 483
111. Elastic scattering in a Coulomb field 492
112. Exchange effects in elastic scattering of identical spin-zero particles 497
113. Exchange effects in elastic scattering of identical particles with spin 499
114. General theory of inelastic scattering 502
115. Scattering of an electron by an atom, neglecting exchange 506
116. Theory of collisions involving rearrangements of particles reactions
117. Scattering of an electron by a hydrogen atom, including exchange 513
118. The scattering matrix 515
119. Time reversal and detailed balancing 524
120. Scattering of slow neutrons by atomic nuclei 531
121. Scattering of polarised nucleons and polarisation of nucleons when scattered by zero-spin nuclei 536
122. Theory of scattering when two kinds of interaction are present distorted wave approximation
123. Dispersion relations in scattering theory 542
124. The scattering matrix in the complex angular momentum plane 553
125. Potential and resonance scattering 557
126. Coherent and incoherent scattering of slow neutrons 559
127. Coherent scattering of neutrons by crystalline substances 563
128. Elastic scattering of slow neutrons by crystals, including atomic vibrations 567
Problems 572
CHAPTER XV. ELEMENTARY THEORY OF MOLECULES AND CHEMICAL BONDS 574
129. Theory of the adiabatic approximation 574
130. The hydrogen molecule 580
131. Elementary theory of chemical forces 588
132. Classification of molecular electronic states when the positions of the nuclei are fixed 596
133. Nuclear vibrations in molecules 600
134. Rotational energy of molecules 605
135. Types of coupling of angular momenta in molecules 612
136. Molecular spectra Franck-Condon principle
Problems 622
MATHEMATICAL APPENDICES 624
A. Some properties of the Dirac delta-function 624
B. The angular momentum operators in spherical coordinates 627
C. Linear operators in a vector space matrices
D. Confluent hypergeometric functions Bessel functions
E. Group theory 640
INDEX 646

Produkt-Details

• Erscheint lt. Verlag: 22.10.2013
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Mechanik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
• Themenwelt: Technik
• ISBN-10: 1-4831-8783-7 / 1483187837
• ISBN-13: 978-1-4831-8783-9 / 9781483187839