Quantum Mechanics: Non-Relativistic TheoryThis edition has been completely revised to include some 20% of new material. Important recent developments such as the theory of Regge poles are now included. Many problems with solutions have been added to those already contained in the book. |
Contents
THE BASIC CONCEPTS OF QUANTUM MECHANICS | 1 |
2 The principle of superposition | 6 |
3 Operators | 8 |
4 Addition and multiplication of operators | 13 |
5 The continuous spectrum | 15 |
6 The passage to the limiting case of classical mechanics | 19 |
7 The wave function and measurements | 21 |
ENERGY AND MOMENTUM | 25 |
81 Valency | 309 |
82 Vibrational and rotational structures of singlet terms in the diatomic molecule | 316 |
83 Multiplet terms Case a | 321 |
84 Multiplet terms Case b | 325 |
85 Multiplet terms Cases c and d | 329 |
86 Symmetry of molecular terms | 331 |
87 Matrix elements for the diatomic molecule | 334 |
88 Adoubling | 338 |
9 The differentiation of operators with respect to time | 26 |
10 Stationary states | 27 |
11 Matrices | 30 |
12 Transformation of matrices | 35 |
13 The Heisenberg representation of operators | 37 |
14 The density matrix | 38 |
15 Momentum | 41 |
16 Uncertainty relations | 45 |
SCHRODINGERS EQUATION | 50 |
18 The fundamental properties of Schrodingers equation | 53 |
19 The current density | 55 |
20 The variational principle | 58 |
21 General properties of motion in one dimension | 60 |
22 The potential well | 63 |
23 The linear oscillator | 67 |
24 Motion in a homogeneous field | 74 |
25 The transmission coefficient | 76 |
ANGULAR MOMENTUM | 82 |
27 Eigenvalues of the angular momentum | 86 |
28 Eigenfunctions of the angular momentum | 89 |
29 Matrix elements of vectors | 92 |
30 Parity of a state | 96 |
31 Addition of angular momenta | 99 |
MOTION IN A CENTRALLY SYMMETRIC FIELD | 102 |
33 Spherical waves | 105 |
34 Resolution of a plane wave | 112 |
35 Fall of a particle to the centre | 114 |
36 Motion in a Coulomb field spherical polar coordinates | 117 |
37 Motion in a Coulomb field parabolic coordinates | 129 |
PERTURBATION THEORY | 133 |
39 The secular equation | 138 |
40 Perturbations depending on time | 142 |
41 Transitions under a perturbation acting for a finite time | 146 |
42 Transitions under the action of a periodic perturbation | 151 |
43 Transitions in the continuous spectrum | 154 |
44 The uncertainty relation for energy | 157 |
45 Potential energy as a perturbation | 159 |
THE QUASICLASSICAL CASE | 164 |
47 Boundary conditions in the quasiclassical case | 167 |
48 Bohr and Sommerfelds quantization rule | 170 |
49 Quasiclassical motion in a centrally symmetric field | 175 |
50 Penetration through a potential barrier | 179 |
51 Calculation of the quasiclassical matrix elements | 185 |
52 The transition probability in the quasiclassical case | 191 |
53 Transitions under the action of adiabatic perturbations | 195 |
SPIN | 199 |
55 The spin operator | 203 |
56 Spinors | 206 |
57 The wave functions of particles with arbitrary spin | 210 |
58 The operator of finite rotations | 215 |
59 Partial polarization of particles | 221 |
60 Time reversal and Kramers theorem | 223 |
IDENTITY OF PARTICLES | 227 |
62 Exchange interaction | 230 |
63 Symmetry with respect to interchange | 234 |
64 Second quantization The case of Bose statistics | 241 |
65 Second quantization The case of Fermi statistics | 247 |
THE ATOM | 251 |
67 Electron states in the atom | 252 |
68 Hydrogenlike energy levels | 256 |
69 The selfconsistent field | 257 |
70 The ThomasFermi equation | 261 |
71 Wave functions of the outer electrons near the nucleus | 266 |
72 Fine structure of atomic levels | 267 |
73 The Mendeleev periodic system | 271 |
74 Xray terms | 279 |
75 Multipole moments | 281 |
76 An atom in an electric field | 284 |
77 A hydrogen atom in an electric field | 289 |
THE DIATOMIC MOLECULE | 300 |
79 The intersection of electron terms | 302 |
80 The relation between molecular and atomic terms | 305 |
89 The interaction of atoms at large distances | 341 |
90 Predissociation | 344 |
THE THEORY OF SYMMETRY | 356 |
92 Transformation groups | 359 |
93 Point groups | 362 |
94 Representations of groups | 370 |
95 Irreducible representations of point groups | 378 |
96 Irreducible representations and the classification of terms | 382 |
97 Selection rules for matrix elements | 385 |
98 Continuous groups | 389 |
99 Twovalued representations of finite point groups | 393 |
POLYATOMIC MOLECULES | 396 |
101 Vibrational energy levels | 403 |
102 Stability of symmetrical configurations of the molecule | 405 |
103 Quantization of the rotation of a top | 410 |
104 The interaction between the vibrations and the rotation of the molecule | 419 |
105 The classification of molecular terms | 423 |
ADDITION OF ANGULAR MOMENTA | 431 |
107 Matrix elements of tensors | 439 |
108 6jsymbols | 442 |
109 Matrix elements for addition of angular momenta | 448 |
110 Matrix elements for axially symmetric systems | 450 |
MOTION IN A MAGNETIC FIELD | 453 |
112 Motion in a uniform magnetic field | 456 |
113 An atom in a magnetic field | 461 |
114 Spin in a variable magnetic field | 468 |
115 The current density in a magnetic field | 470 |
NUCLEAR STRUCTURE | 472 |
117 Nuclear forces | 476 |
118 The shell model | 480 |
119 Nonspherical nuclei | 489 |
120 Isotopic shift | 494 |
121 Hyperfine structure of atomic levels | 496 |
122 Hyperfine structure of molecular levels | 499 |
ELASTIC COLLISIONS | 502 |
124 An investigation of the general formula | 506 |
125 The unitarity condition for scattering | 509 |
126 Borns formula | 513 |
127 The quasiclassical case | 519 |
128 Analytical properties of the scattering amplitude | 524 |
129 The dispersion relation | 530 |
130 The scattering amplitude in the momentum representation | 533 |
131 Scattering at high energies | 536 |
132 The scattering of slow particles | 543 |
133 Resonance scattering at low energies | 550 |
134 Resonance at a quasidiscrete level | 557 |
135 Rutherfords formula | 562 |
136 The system of wave functions of the continuous spectrum | 565 |
137 Collisions of like particles | 569 |
138 Resonance scattering of charged particles | 572 |
139 Elastic collisions between fast electrons and atoms | 577 |
140 Scattering with spinorbit interaction | 581 |
141 Regge poles | 587 |
INELASTIC COLLISIONS | 593 |
143 Inelastic scattering of slow particles | 599 |
144 The scattering matrix in the presence of reactions | 601 |
145 Breit and Wigners formulae | 605 |
146 Interaction in the final state in reactions | 613 |
147 Behaviour of crosssections near the reaction threshold | 616 |
148 Inelastic collisions between fast electrons and atoms | 620 |
149 The effective retardation | 629 |
150 Inelastic collisions between heavy particles and atoms | 633 |
151 Scattering of neutrons | 634 |
152 Inelastic scattering at high energies | 638 |
MATHEMATICAL APPENDICES | 645 |
b The Airy function | 648 |
c Legendre polynomials | 650 |
d The confluent hypergeometric function | 653 |
e The hypergeometric function | 657 |
f The calculation of integrals containing confluent hypergeometric functions | 660 |
Index | 665 |
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Common terms and phrases
according angle antisymmetrical approximation asymptotic atom axes axis calculated classical mechanics coefficient collision commutation complex conjugate components condition constant continuous spectrum coordinates corresponding Coulomb field definite values degeneracy denote dependence derived determined diagonal direction discrete spectrum eigenfunctions eigenvalues elastic scattering electron terms energy levels exponentially expression factor finite formula gives Hamiltonian Hence inelastic infinity integral interaction irreducible representations linear matrix elements mean value molecule momenta motion neutron non-zero normal nuclear nucleons nucleus obtain operator orbital angular momentum particle perturbation theory physical quantity plane potential energy probability PROBLEM properties protons quantum mechanics quantum number quasi-classical region relation respect result rotation scalar scattering amplitude scattering cross-section Schrödinger's equation SOLUTION spherical spinor spinor of rank stationary Substituting suffixes symmetry tensor total angular momentum total spin transformation transition variables vector velocity vibrations wave function z-axis zero