Quantum Mechanics: NonRelativistic 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. 
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Table des matières
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 
671  
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Expressions et termes fréquents
according angle antisymmetrical approximation atom axes axis calculated classical mechanics coefficient collision commute complex conjugate components condition constant continuous spectrum coordinates corresponding Coulomb field definite values degeneracy denote density dependence derived determined diagonal direction discrete spectrum eigenfunctions eigenvalues elastic scattering electron terms energy levels exponentially factor finite formula gives Hamiltonian Hence infinity integral interaction irreducible representations large distances linear magnetic moment matrix elements mean value molecule momenta motion neutrons nonzero normal nuclear nucleons nucleus obtain operator orbital angular momentum parameter particles perturbation theory physical quantity plane possible values potential energy probability PROBLEM properties protons quantum mechanics quantum number quasiclassical region relation respect result rotation scalar scattering amplitude scattering crosssection Schrodinger'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 zero