Introduction and orientation |
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1 | (1) |
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1 | (2) |
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3 | (1) |
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The photoelectric and Compton effects |
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4 | (1) |
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5 | (1) |
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6 | (2) |
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8 | (1) |
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The foundations of quantum mechanics |
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9 | (34) |
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Operators in quantum mechanics |
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9 | (10) |
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10 | (1) |
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Eigenfunctions and eigenvalues |
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10 | (2) |
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12 | (1) |
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Commutation and non-commutation |
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13 | (1) |
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The construction of operators |
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14 | (1) |
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15 | (1) |
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16 | (1) |
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17 | (2) |
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The postulates of quantum mechanics |
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19 | (6) |
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19 | (1) |
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The fundamental prescription |
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20 | (1) |
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The outcome of measurements |
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20 | (2) |
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The interpretation of the wavefunction |
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22 | (1) |
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The equation for the wavefunction |
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23 | (1) |
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The separation of the Schrodinger equation |
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23 | (2) |
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The specification and evolution of states |
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25 | (7) |
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25 | (2) |
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The uncertainty principle |
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27 | (2) |
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Consequences of the uncertainty principle |
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29 | (1) |
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The uncertainty in energy and time |
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30 | (1) |
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Time-evolution and conservation laws |
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30 | (2) |
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Matrices in quantum mechanics |
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32 | (4) |
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32 | (2) |
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The diagonalization of the hamiltonian |
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34 | (2) |
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The plausibility of the Schrodinger equation |
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36 | (7) |
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36 | (2) |
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The propagation of particles |
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38 | (1) |
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The transition to quantum mechanics |
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39 | (1) |
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40 | (3) |
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Linear motion and the harmonic oscillator |
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43 | (28) |
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The characteristics of acceptable wavefunctions |
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43 | (1) |
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Some general remarks on the Schrodinger equation |
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44 | (3) |
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The curvature of the wavefunction |
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45 | (1) |
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45 | (1) |
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The emergence of quantization |
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46 | (1) |
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Penetration into non-classical regions |
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46 | (1) |
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47 | (4) |
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48 | (1) |
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The significance of the coefficients |
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48 | (1) |
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49 | (1) |
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50 | (1) |
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Penetration into and through barriers |
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51 | (4) |
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An infinitely thick potential wall |
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51 | (1) |
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A barrier of finite width |
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52 | (2) |
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The Eckart potential barrier |
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54 | (1) |
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55 | (5) |
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56 | (1) |
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Features of the solutions |
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57 | (1) |
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The two-dimensional square well |
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58 | (1) |
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59 | (1) |
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60 | (6) |
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61 | (2) |
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Properties of the solutions |
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63 | (2) |
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65 | (1) |
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Translation revisited: The scattering matrix |
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66 | (5) |
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68 | (3) |
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Rotational motion and the hydrogen atom |
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71 | (27) |
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71 | (5) |
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The hamiltonian and the Schrodinger equation |
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71 | (2) |
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73 | (1) |
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The shapes of the wavefunctions |
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74 | (2) |
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76 | (1) |
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76 | (8) |
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The Schrodinger equation and its solution |
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76 | (3) |
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The angular momentum of the particle |
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79 | (2) |
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Properties of the solutions |
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81 | (1) |
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82 | (2) |
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Motion in a Coulombic field |
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84 | (14) |
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The Schrodinger equation for hydrogenic atoms |
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84 | (1) |
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The separation of the relative coordinates |
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85 | (1) |
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The radial Schrodinger equation |
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85 | (5) |
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Probabilities and the radial distribution function |
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90 | (1) |
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91 | (3) |
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The degeneracy of hydrogenic atoms |
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94 | (2) |
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96 | (2) |
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98 | (24) |
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The angular momentum operators |
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98 | (4) |
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The operators and their commutation relations |
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99 | (2) |
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Angular momentum observables |
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101 | (1) |
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101 | (1) |
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The definition of the states |
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102 | (10) |
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The effect of the shift operators |
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102 | (2) |
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The eigenvalues of the angular momentum |
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104 | (2) |
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The matrix elements of the angular momentum |
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106 | (2) |
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The angular momentum eigenfunctions |
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108 | (2) |
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110 | (2) |
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The angular momenta of composite systems |
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112 | (10) |
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The specification of coupled states |
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112 | (1) |
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The permitted values of the total angular momentum |
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113 | (2) |
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The vector model of coupled angular momenta |
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115 | (2) |
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The relation between schemes |
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117 | (2) |
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The coupling of several angular momenta |
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119 | (1) |
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120 | (2) |
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122 | (46) |
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The symmetries of objects |
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122 | (7) |
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Symmetry operations and elements |
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123 | (1) |
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The classification of molecules |
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124 | (5) |
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129 | (16) |
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The definition of a group |
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129 | (1) |
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Group multiplication tables |
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130 | (1) |
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131 | (4) |
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The properties of matrix representations |
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135 | (2) |
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The characters of representations |
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137 | (1) |
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138 | (1) |
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Irreducible representations |
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139 | (3) |
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The great and little orthogonality theorems |
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142 | (3) |
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145 | (6) |
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The reduction of representations |
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146 | (1) |
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147 | (4) |
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The symmetry properties of functions |
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151 | (10) |
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The transformation of p-orbitals |
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151 | (1) |
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The decomposition of direct-product bases |
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152 | (3) |
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155 | (2) |
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157 | (2) |
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159 | (2) |
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161 | (4) |
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The generators of rotations |
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161 | (1) |
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The representation of the full rotation group |
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162 | (2) |
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164 | (1) |
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165 | (3) |
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166 | (2) |
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Techniques of approximation |
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168 | (39) |
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Time-independent perturbation theory |
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168 | (15) |
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Perturbation of a two-level system |
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169 | (2) |
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171 | (1) |
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The first-order correction to the energy |
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172 | (2) |
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The first-order correction to the wavefunction |
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174 | (1) |
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The second-order correction to the energy |
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175 | (1) |
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Comments on the perturbation expressions |
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176 | (2) |
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The closure approximation |
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178 | (2) |
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Perturbation theory for degenerate states |
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180 | (3) |
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183 | (4) |
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183 | (2) |
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185 | (2) |
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The Hellmann-Feynman theorem |
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187 | (2) |
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Time-dependent perturbation theory |
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189 | (18) |
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The time-dependent behaviour of a two-level system |
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189 | (3) |
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192 | (1) |
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Many-level systems: the variation of constants |
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193 | (2) |
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The effect of a slowly switched constant perturbation |
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195 | (2) |
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The effect of an oscillating perturbation |
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197 | (2) |
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Transition rates to continuum states |
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199 | (1) |
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The Einstein transition probabilities |
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200 | (3) |
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Lifetime and energy uncertainty |
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203 | (1) |
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204 | (3) |
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Atomic spectra and atomic structure |
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207 | (42) |
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The spectrum of atomic hydrogen |
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207 | (12) |
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The energies of the transitions |
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208 | (1) |
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209 | (3) |
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Orbital and spin magnetic moments |
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212 | (2) |
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214 | (2) |
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The fine-structure of spectra |
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216 | (1) |
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Term symbols and spectral details |
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217 | (1) |
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The detailed spectrum of hydrogen |
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218 | (1) |
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219 | (10) |
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219 | (3) |
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222 | (2) |
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224 | (1) |
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225 | (4) |
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229 | (13) |
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Penetration and shielding |
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229 | (2) |
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231 | (2) |
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233 | (1) |
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234 | (2) |
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Term symbols and transitions of many-electron atoms |
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236 | (3) |
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Hund's rules and the relative energies of terms |
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239 | (1) |
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Alternative coupling schemes |
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240 | (2) |
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242 | (7) |
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242 | (1) |
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The anomalous Zeeman effect |
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243 | (2) |
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245 | (1) |
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246 | (3) |
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An introduction to molecular structure |
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249 | (38) |
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The Born-Oppenheimer approximation |
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249 | (4) |
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The formulation of the approximation |
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250 | (1) |
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An application: the hydrogen molecule-ion |
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251 | (2) |
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253 | (13) |
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Linear combinations of atomic orbitals |
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253 | (5) |
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258 | (1) |
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Configuration interaction |
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259 | (2) |
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261 | (4) |
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Heteronuclear diatomic molecules |
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265 | (1) |
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Molecular orbital theory of polyatomic molecules |
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266 | (12) |
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Symmetry-adapted linear combinations |
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266 | (3) |
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269 | (5) |
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274 | (2) |
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Further aspects of ligand field theory |
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276 | (2) |
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The band theory of solids |
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278 | (9) |
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The tight-binding approximation |
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279 | (2) |
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281 | (3) |
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284 | (1) |
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285 | (2) |
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The calculation of electronic structure |
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287 | (55) |
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The Hartree-Fock self-consistent field method |
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288 | (14) |
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The formulation of the approach |
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288 | (1) |
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The Hartree-Fock approach |
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289 | (2) |
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Restricted and unrestricted Hartree-Fock calculations |
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291 | (2) |
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293 | (3) |
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The selection of basis sets |
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296 | (5) |
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Calculational accuracy and the basis set |
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301 | (1) |
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302 | (14) |
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Configuration state functions |
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303 | (1) |
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Configuration interaction |
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303 | (2) |
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305 | (3) |
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Multiconfiguration and multireference methods |
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308 | (2) |
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Moller-Plesset many-body perturbation theory |
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310 | (3) |
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The coupled-cluster method |
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313 | (3) |
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Density functional theory |
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316 | (5) |
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Kohn-Sham orbitals and equations |
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317 | (2) |
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Exchange-correlation functionals |
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319 | (2) |
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Gradient methods and molecular properties |
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321 | (4) |
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Energy derivatives and the Hessian matrix |
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321 | (1) |
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Analytical derivatives and the coupled perturbed equations |
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322 | (3) |
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325 | (7) |
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Conjugated π-electron systems |
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326 | (3) |
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Neglect of differential overlap |
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329 | (3) |
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332 | (4) |
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333 | (1) |
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Quantum mechanics-molecular mechanics |
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334 | (2) |
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Software packages for electronic structure calculations |
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336 | (6) |
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339 | (3) |
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Molecular rotations and vibrations |
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342 | (40) |
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Spectroscopic transitions |
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342 | (2) |
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342 | (2) |
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344 | (1) |
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344 | (13) |
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345 | (4) |
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349 | (1) |
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Pure rotational selection rules |
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349 | (2) |
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Rotational Raman selection rules |
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351 | (2) |
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353 | (4) |
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The vibrations of diatomic molecules |
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357 | (8) |
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The vibrational energy levels of diatomic molecules |
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357 | (2) |
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359 | (1) |
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Vibrational selection rules |
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360 | (2) |
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Vibration-rotation spectra of diatomic molecules |
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362 | (2) |
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Vibrational Raman transitions of diatomic molecules |
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364 | (1) |
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The vibrations of polyatomic molecules |
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365 | (14) |
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365 | (3) |
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Vibrational selection rules for polyatomic molecules |
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368 | (1) |
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Group theory and molecular vibrations |
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369 | (4) |
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The effects of anharmonicity |
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373 | (3) |
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376 | (1) |
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377 | (2) |
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Appendix 10.1 Centrifugal distortion |
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379 | (3) |
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380 | (2) |
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Molecular electronic transitions |
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382 | (25) |
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The states of diatomic molecules |
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382 | (4) |
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382 | (2) |
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Decoupling and A-doubling |
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384 | (2) |
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386 | (1) |
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386 | (4) |
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The Franck-Condon principle |
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386 | (3) |
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The rotational structure of vibronic transitions |
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389 | (1) |
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The electronic spectra of polyatomic molecules |
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390 | (6) |
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391 | (1) |
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391 | (2) |
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Vibronically allowed transitions |
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393 | (2) |
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Singlet-triplet transitions |
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395 | (1) |
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The fate of excited species |
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396 | (11) |
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396 | (1) |
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397 | (2) |
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The conservation of orbital symmetry |
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399 | (1) |
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399 | (2) |
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401 | (2) |
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Photochemically induced electrocyclic reactions |
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403 | (1) |
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Photochemically induced cycloaddition reactions |
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404 | (2) |
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406 | (1) |
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The electric properties of molecules |
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407 | (29) |
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The response to electric fields |
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407 | (11) |
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Molecular response parameters |
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407 | (2) |
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The static electric polarizability |
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409 | (2) |
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Polarizability and molecular properties |
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411 | (2) |
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Polarizabilities and molecular spectroscopy |
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413 | (1) |
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Polarizabilities and dispersion forces |
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414 | (4) |
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418 | (1) |
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Bulk electrical properties |
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418 | (9) |
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The relative permittivity and the electric susceptibility |
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418 | (2) |
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420 | (2) |
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422 | (5) |
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427 | (9) |
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Circular birefringence and optical rotation |
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427 | (2) |
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Magnetically induced polarization |
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429 | (2) |
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431 | (3) |
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434 | (2) |
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The magnetic properties of molecules |
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436 | (37) |
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The descriptions of magnetic fields |
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436 | (6) |
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The magnetic susceptibility |
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436 | (1) |
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437 | (2) |
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439 | (1) |
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Derivatives of vector functions |
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440 | (1) |
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441 | (1) |
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442 | (10) |
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The perturbation hamiltonian |
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442 | (2) |
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The magnetic susceptibility |
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444 | (3) |
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447 | (3) |
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The diamagnetic current density |
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450 | (1) |
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The paramagnetic current density |
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451 | (1) |
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Magnetic resonance parameters |
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452 | (21) |
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452 | (4) |
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The diamagnetic contribution to shielding |
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456 | (2) |
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The paramagnetic contribution to shielding |
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458 | (1) |
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459 | (3) |
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462 | (1) |
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463 | (4) |
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Nuclear spin-spin coupling |
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467 | (4) |
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471 | (2) |
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473 | (40) |
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The formulation of scattering events |
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473 | (6) |
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The scattering cross-section |
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473 | (2) |
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Stationary scattering states |
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475 | (4) |
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Partial-wave stationary scattering states |
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479 | (18) |
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479 | (1) |
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The partial-wave equation |
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480 | (1) |
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Free-particle radial wavefunctions and the scattering phase shift |
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481 | (3) |
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The JWKB approximation and phase shifts |
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484 | (2) |
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Phase shifts and the scattering matrix element |
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486 | (2) |
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Phase shifts and scattering cross-sections |
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488 | (2) |
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Scattering by a spherical square well |
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490 | (2) |
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Background and resonance phase shifts |
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492 | (2) |
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494 | (1) |
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Resonance contributions to the scattering matrix element |
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495 | (2) |
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497 | (5) |
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497 | (1) |
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Multichannel stationary scattering states |
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498 | (1) |
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498 | (3) |
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The S matrix and multichannel resonances |
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501 | (1) |
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502 | (6) |
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The integral scattering equation and Green's functions |
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502 | (2) |
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504 | (4) |
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Appendix 14.1 The derivation of the Breit-Wigner formula |
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508 | (1) |
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Appendix 14.2 The rate constant for reactive scattering |
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509 | (4) |
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510 | (3) |
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513 | (40) |
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513 | (6) |
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513 | (2) |
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515 | (1) |
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516 | (2) |
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518 | (1) |
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Solutions of the Schrodinger equation |
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519 | (15) |
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The motion of wavepackets |
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519 | (2) |
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The harmonic oscillator: solution by factorization |
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521 | (2) |
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The harmonic oscillator: the standard solution |
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523 | (2) |
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525 | (1) |
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526 | (1) |
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527 | (1) |
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The Hartree--Fock equations |
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528 | (4) |
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532 | (1) |
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The unitarity of the S matrix |
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533 | (1) |
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Group theory and angular momentum |
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534 | (3) |
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The orthogonality of basis functions |
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534 | (1) |
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Vector coupling coefficients |
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535 | (2) |
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537 | (6) |
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Electric dipole transitions |
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537 | (1) |
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538 | (2) |
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540 | (1) |
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541 | (2) |
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The electromagnetic field |
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543 | (4) |
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543 | (3) |
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The dipolar vector potential |
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546 | (1) |
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547 | (6) |
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547 | (2) |
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549 | (4) |
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553 | (4) |
Appendix 1 |
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557 | (5) |
Appendix 2 |
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562 | (1) |
Answers to selected problems |
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563 | (2) |
Index |
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565 | |