Quantum Mechanics: Non-relativistic Theory

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Butterworth-Heinemann, 1977 - Science - 677 pages
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This 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.


  

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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
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
ADDITION OF ANGULAR MOMENTA
433
107 Matrix elements of tensors
441
108 6jsymbols
444
109 Matrix elements for addition of angular momenta
450
110 Matrix elements for axially symmetric systems
452
MOTION 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
NUCLEAR STRUCTURE
474
117 Nuclear forces
478
118 The shell model
482
119 Nonspherical nuclei
491
120 Isotopic shift
496
121 Hyperfine structure of atomic levels
498
122 Hyperfine structure of molecular levels
501
ELASTIC COLLISIONS
504
124 An investigation of the general formula
508
125 The unitarity condition for scattering
511
126 Borns formula
515
127 The quasiclassical 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 quasidiscrete level
559
135 Rutherfords 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 spinorbit interaction
583
141 Regge poles
589
INELASTIC COLLISIONS
595
143 Inelastic scattering of slow particles
601
144 The scattering matrix in the presence of reactions
603
145 Breit and Wigners formulae
607
146 Interaction in the final state in reactions
615
147 Behaviour of crosssections 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
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
Copyright

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About the author (1977)

Lev Davidovich Landau was born on January 22, 1908 in Baku, U.S.S.R (now Azerbaijan). A brilliant student, he had finished secondary school by the age of 13. He enrolled in the University of Baku a year later, in 1922, and later transferred to the University of Leningrad, from which he graduated with a degree in physics. Landau did graduate work in physics at Leningrad's Physiotechnical Institute, at Cambridge University in England, and at the Institute of Theoretical Physics in Denmark, where he met physicist Neils Bohr, whose work he greatly admired. Landau worked in the Soviet Union's nuclear weapons program during World War II, and then began a teaching career. Considered to be the founder of a whole school of Soviet theoretical physicists, Landau was honored with numerous awards, including the Lenin Prize, the Max Planck Medal, the Fritz London Prize, and, most notably, the 1962 Nobel Prize for Physics, which honored his pioneering work in the field of low-temperature physics and condensed matter, particularly liquid helium. Unfortunately, Landau's wife and son had to accept the Nobel Prize for him; Landau had been seriously injured in a car crash several months earlier and never completely recovered. He was unable to work again, and spent the remainder of his years, until his death in 1968, battling health problems resulting from the accident. Landau's most notable written work is his Course of Theoretical Physics, an eight-volume set of texts covering the complete range of theoretical physics. Like several other of Landau's books, it was written with Evgeny Lifshitz, a favorite student, because Landau himself strongly disliked writing. Some other works include What is Relativity?, Theory of Elasticity, and Physics for Everyone.