Ctp Vol 3 Quantum Mechanics Book

	From the Preface to the first English edition	xi
	Preface to the second English edition	xii
	Preface to the third Russian edition	xiii
	Editor's Preface to the fourth Russian edition	xiv
	Notation	xv
I.	The Basic Concepts of Quantum Mechanics
1.	The uncertainty principle	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
II.	Energy and Momentum
8.	The Hamiltonian operator	25
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
III.	Schrodinger's Equation
17.	Schrodinger's equation	50
18.	The fundamental properties of Schrodinger's 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
IV.	Angular Momentum
26.	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
V.	Motion in a Centrally Symmetric Field
32.	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
VI.	Perturbation Theory
38.	Perturbations independent of time	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
VII.	The Quasi-Classical Case
46.	The wave function in the quasi-classical case	164
47.	Boundary conditions in the quasi-classical case	167
48.	Bohr and Sommerfeld's quantization rule	170
49.	Quasi-classical motion in a centrally symmetric field	175
50.	Penetration through a potential barrier	179
51.	Calculation of the quasi-classical matrix elements	185
52.	The transition probability in the quasi-classical case	191
53.	Transitions under the action of adiabatic perturbations	195
VIII.	Spin
54.	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
IX.	Identity of Particles
61.	The principle of indistinguishability of similar 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
X.	The Atom
66.	Atomic energy levels	251
67.	Electron states in the atom	252
68.	Hydrogen-like energy levels	256
69.	The self-consistent field	257
70.	The Thomas-Fermi 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.	X-ray terms	279
75.	Multipole moments	281
76.	An atom in an electric field	284
77.	A hydrogen atom in an electric field	289
XI.	The Diatomic Molecule
78.	Electron terms in the diatomic molecule	300
79.	The intersection of electron terms	302
80.	The relation between molecular and atomic terms	305
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.	A-doubling	338
89.	The interaction of atoms at large distances	341
90.	Pre-dissociation	344
XII.	The Theory of Symmetry
91.	Symmetry transformations	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.	Two-valued representations of finite point groups	393
XIII.	Polyatomic Molecules
100.	The classification of molecular vibrations	398
101.	Vibrational energy levels	405
102.	Stability of symmetrical configurations of the molecule	407
103.	Quantization of the rotation of a top	412
104.	The interaction between the vibrations and the rotation of the molecule	421
105.	The classification of molecular terms	425
XIV.	Addition of Angular Momenta
106.	3j-symbols	433
107.	Matrix elements of tensors	441
108.	6j-symbols	444
109.	Matrix elements for addition of angular momenta	450
110.	Matrix elements for axially symmetric systems	452
XV.	Motion in a Magnetic Field
111.	Schrodinger's equation in a magnetic field	455
112.	Motion in a uniform magnetic field	458
113.	An atom in a magnetic field	463
114.	Spin in a variable magnetic field	470
115.	The current density in a magnetic field	472
XVI.	Nuclear Structure
116.	Isotopic invariance	474
117.	Nuclear forces	478
118.	The shell model	482
119.	Non-spherical nuclei	491
120.	Isotopic shift	496
121.	Hyperfine structure of atomic levels	498
122.	Hyperfine structure of molecular levels	501
XVII.	Elastic Collisions
123.	The general theory of scattering	504
124.	An investigation of the general formula	508
125.	The unitarity condition for scattering	511
126.	Born's formula	515
127.	The quasi-classical case	521
128.	Analytical properties of the scattering amplitude	526
129.	The dispersion relation	532
130.	The scattering amplitude in the momentum representation	535
131.	Scattering at high energies	538
132.	The scattering of slow particles	545
133.	Resonance scattering at low energies	552
134.	Resonance at a quasi-discrete level	559
135.	Rutherford's formula	564
136.	The system of wave functions of the continuous spectrum	567
137.	Collisions of like particles	571
138.	Resonance scattering of charged particles	574
139.	Elastic collisions between fast electrons and atoms	579
140.	Scattering with spin-orbit interaction	583
141.	Regge poles	589
XVIII.	Inelastic Collisions
142.	Elastic scattering in the presence of inelastic processes	595
143.	Inelastic scattering of slow particles	601
144.	The scattering matrix in the presence of reactions	603
145.	Breit and Wigner's formulae	607
146.	Interaction in the final state in reactions	615
147.	Behaviour of cross-sections near the reaction threshold	618
148.	Inelastic collisions between fast electrons and atoms	624
149.	The effective retardation	633
150.	Inelastic collisions between heavy particles and atoms	637
151.	Scattering of neutrons	640
152.	Inelastic scattering at high energies	644
	Mathematical Appendices
a.	Hermite polynomials	651
b.	The Airy function	654
c.	Legendre polynomials	656
d.	The confluent hypergeometric function	659
e.	The hypergeometric function	663
f.	The calculation of integrals containing confluent hypergeometric functions	666
	Index	671