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| Ïîèñê ïî óêàçàòåëÿì |
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| Beard D.B. — Quantum Mechanics |
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| Ïðåäìåòíûé óêàçàòåëü |
Absorption, radiation 190—192
Absorption, radiation with ionization 203—205
Absorption, rate per unit volume 199
Action, classical 56
Alpha particle decay 91 92 122
Amplitude (see Probability amplitude)
Angular momentum and spin addition 259 260
Angular momentum, addition of 254—260
Angular momentum, commutation relations 136—138
Angular momentum, eigenvalues 132—133 140
Angular momentum, light 194—195
Angular momentum, matrix representation 235—238
Angular momentum, operators 130—132
Angular wave functions in spherical coordinates 127—129
Antisymmetric spin state 246
Antisymmetric wave function 246
Antisymmetric wave function, first excited state of helium atom 221—222
Approximation, Bom scattering cross-sections 269—279
Approximation, slowly varying potential (semiclassical) 110—117
Approximation, time dependent perturbation theory 184—198
Approximation, time independent perturbation theory 161—175
Approximation, variational method 179—182
Approximation, Wentzel-Kramers-Brillouin (WKB) 110—117
Associated Laguerre functions 148
Associated Legendre functions 127—129 134—136 139
Associated spherical harmonics 126—129
Atomic excitation by ion bombardment 188—190
Atomic excitation, radiative absorption 190—192
Atomic form factor 278 279
Average energy of mode of oscillation 8—12
Average value 68
Azimuthal angular wave function 127
Babinet’s theorem 268
Balmer formula 148 149
Band theory of metals 99—106
Barrier penetration, square barrier 85—92
Barrier penetration, WKB approximation 121—123
Bessel function one-half order 142—145
Bessel function one-third order 113 114
Bessel function spherical 142—145
Beta-decay, conservation of parity 252—254
BKW approximation 110—117 (see also Wentzel-Kramers-Brillouin)
Bloch wave function 102—104
Bohr, Niels, atomic orbits 46
Bohr, Niels, description of light diffraction 41
Bohr, Niels, frequency condition 187
Bohr-Sommerfeld quantum conditions 117—120
Boltzmann constant 8
Bom approximation 269—279
Bound particles in a square well 94—98
boundary conditions 4 12
Bra-vector 216—217
Bragg x-ray diffraction 46
Center of mass coordinates 78—81
Center of mass motion equation 80
Characteristic functions 13 (see also Eigenfunctions)
Characteristic values 13 (see also Eigenvalues)
Chemical binding 208—209
Classical action 56
Classical path taken by particle or light ray 111
Clebsch — Gordon coefficients 254—260
Commutation relations 71—76
Commutation relations, angular momentum 136—138
Commutation relations, between coordinate and momentum 72
Commutation relations, spin 243
Commutator 72
Commuting operators, diagonal representation 238—245
Complementary variables 16 34
Complete set 158 159
Compton effect 36—38
Compton wavelength 38
Continuity equation 77 78
Cosine series 17—19
Coulomb integrals 218 219
Coulomb integrals, hydrogen molecule 224—225
Coulomb potential, scattering crosssection 275 276
Cross-sections, scattering (see Scattering cross-sections)
Currents, particles 77 78
Davisson — Germer experiment 45 46 49—52
de Broglie wavelength 46
Degeneracy in spherical harmonic oscillator 154
Degenerate perturbation theory 171—175
Degenerate perturbation theory, harmonic oscillators 213—216
Degenerate perturbation theory, helium atom, first excited state 218—222
Degenerate perturbation theory, hydrogen molecule 222—226
Delta-function, Dirac 21
Delta-function, Kronecker 17
Deuteron 97 98
Diagonal operators, commutation of 238
Diagonalization of an operator 234
Diffraction, electrons 45—46 49—52
Diffraction, light (interference of photons) 38—41 52—54
Diffraction, particles 45 46 54—58
Dipole transitions 192—196
Dirac delta-function 21
Dirac notation 216 217
Eckart — Bethe potential 118—120
Effective range 293—294 296
Eigenfunctions 13
Eigenvalues 13 67
Eigenvalues, angular momentum 132 133 140
Einstein A and B coefficients 198—200
Electromagnetic waves in a box 1—6 (see also Radiation)
Electron, angular momentum operator 244—245
Electron, diffraction 45—52
Electron, emission from metals 122 123
Electron, interaction in atoms, general discussion 227—230
Electron, wave functions and energies in a metal 99—106
Emission of radiation 198—200
Energy levels, atomic 148
Energy levels, bound particle in a potential 111
Energy levels, degenerate perturbation theory 171 175
Energy levels, due to spin orbit force 176—178
Energy levels, harmonic oscillator linear 155
Energy levels, helium atom 217 222
Energy levels, hydrogen 148
Energy levels, nuclear potential 118—120 154
Energy levels, spherical 153 154
Energy levels, splitting due to mutual repulsion of electrons 178
Energy levels, square well, spherical 145
Energy operator 68
Exchange integrals 218 219
Exchange integrals, hydrogen molecule 224—225
Exchange operation 245—246
Excitation, atomic by ion bombardment 188—190
Excitation, atomic by radiation 190—192
Exclusion principle, Pauli 247
Expectation 68—70
Expectation of coordinates 68
Expectation, energy 73
Expectation, momentum operator 69
Expectation, momentum operator derivative 75
Expectation, momentum operator of operator 72
Expectation, momentum operator time derivative 73 74
Expectation, time derivative 74 75
Expected value 68
Fermat’s principle 111
Fermi level, Fermi energy 102
Fermi scattering length 288 296
Fine structure 175—178
Fine structure, hydrogen atom 176—178
Form factor, atomic 278 279
Fourier series 17—19
Fourier transform 20—26 271—273
Frequency spread and time duration 23—26
Gaussian distribution function 24—30
Gaussian distribution function, Franck and Hertz experiment 35 36
Gaussian distribution, Fourier transform 20 30
Gaussian wave packet 29 30 65 66
Group velocity 28 65 66
| Hamiltonian 69
Hamilton’s principle function 56 111
Harmonic oscillator, coupled, classical 209—211
Harmonic oscillator, coupled, quantum mechanical 212—216
Harmonic oscillator, linear 155
Harmonic oscillator, selection rules 196 197
Harmonic oscillator, spherical 150—154
Heisenberg uncertainty principle (see Uncertainty principle)
Heitler-London theory, calculation of the hydrogen molecule 222—226
Helium atom, first excited state 217—222
Helium atom, ground state, first order perturbation theory 164—168
Helium atom, ground state, variational method 181 182
Hermite polynomials 154
Hermitian operators 75 76
Hund’s rule 248 249
Hydrogen atom 146—150
Hydrogen atom, fine structure 176—178
Hydrogen atom, selection rules 197 198
Hydrogen atom, wave functions 146 148
hydrogen molecule 222—226
Indices of refraction, particles and light 65
Induced emission 200
Interference of photons 38—41
j-j coupling 230
Ket-vector 217
Kronecker delta 17
Kronnig — Penney potential 102—106
Lagrangian 56
Laguerre functions and polynomials 148
Legendre polynomials (see Associated Legendre functions)
Lienard-Wiechart retarded potential 270—272
Light, angular momentum 194 195
Light, probability amplitude 52—54
Linear independence 171
London-Heitler theory of hydrogen molecule 222—226
Matrices, spin 242—245
Matrix representation, angular momentum 235—238
Matrix representation, operators on eigenfunctions 232—234 235
Maxwell-Boltzmann energy distribution 8
Maxwell’s equations 2
Microscope experiment 41—43
Momentum operator 68 70
Momentum transfer 273
Mott scattering 280—281
Neutron-proton scattering cross-section 277
Newton’s second law, quantum mechanical version 75
Normalization of wave functions 158
Nuclear potential 118—120
Nuclear potential, energy levels 117—120 154
Nuclear potential, wave functions in a harmonic oscillator potential 151—155
Nuclear potential, wave functions in a square well 141—145
Observables, physical 67—71 75 76
Octupole transition 195
Operation 12
Operator 12 67—71
Operator, angular momentum 130—132
Operator, diagonalization 234
Operator, energy 68
Operator, hermitian 75 76
Operator, matrix representation 232 234 235
Operator, momentum 68 70
Operator, position 71
Optical analogue of quantum mechanics 90 91
Orthogonal functions 16 17
Orthogonality 16 17
Orthogonality of wave functions 158—161
Orthogonality, degenerate 171—172
Orthogonalization of eigenfunctions belonging to a degenerate energy level 171 172
oscillators (see Harmonic oscillators)
Oscillators, coupled classical 209—212
Oscillators, quantum mechanical 212—216
Parity 249—254
Parity of eigenfunctions 232
Parity, angular momentum and spin 250
Parity, beta decay 252—254
Parity, conservation 250—254
Partial waves, scattering theory 281—288
Particle, current density 77 78
Particle, probability amplitudes 54—58
Particle, wave characteristics of 41—43
Particle, wave packet 65 66
Particle, waves 64—66
Pauli exclusion principle 247
Pauli theory of spin (spin matrices) 242—245
Penetration through a barrier, square barrier 85—92
Penetration through a barrier, WKB approximation 121—123
Perturbation theory, degenerate 171—175
Perturbation theory, harmonic oscillators 213—216
Perturbation theory, helium atom, first excited state 218—222
Perturbation theory, time dependent, first order 184—187
Perturbation theory, time dependent, second order 201—203
Perturbation theory, time independent, first order 161—164
Perturbation theory, time independent, second order 169—170
phase velocity 28
Photolectric effect 35 45
photons 33—40
Photons, diffraction and interference 38—41
Photons, probability amplitude 52—54
Planck black body distribution 9 11
Planck’s constant 10 11
Plane wave in a string 299—301
Plane wave, expansion in complete orthonormal set 284
Plane wave, expansion in set of spherical harmonic wave functions 195
Position operator 71
Probability amplitude, light 52—54
Probability amplitude, particle 54—58
Probability in volume of momentum space 71
Pseudoscalars 252—253
Pseudovectors 252
Quadrupole transition 195
Quanta 33—40
Radiation, Energy density 8—12
Radiation, number of modes of vibration 6—7
Radiation, pressure 36 37
Radiation, transitions 190—192
Ramsauer effect 93 94
Rayleigh — Jean’s law 9
Reduced mass 79
Reduced mass, effect in scattering cross-sections 274
Refraction index 65
Relative motion equation 80
Resonance integrals 218 219 224 225
Resonance, classical 207 208 211 212
Resonance, energy 220—221
Resonance, helium atom, first excited state 218—222
Resonance, quantum mechanical oscillators 212—216
Rigid rotator 139 140
Russell — Saunders coupling 230 249
Rutherford’s experiment 44
Scattering cross-sections 263—265
Scattering cross-sections, alpha particles 279
Scattering cross-sections, atomic by the Born approximation 277—279
Scattering cross-sections, billiard ball collision by Bom approximation 279
Scattering cross-sections, Bom approximation 269—279
Scattering cross-sections, classical limit 290
Scattering cross-sections, constant potential by Bom approximation 279
Scattering cross-sections, Coulomb potential by Bom approximation 275—279
Scattering cross-sections, differential scattering cross-sections 264—265
Scattering cross-sections, effective range theory 291—296
Scattering cross-sections, Fermi scattering length 288 296
Scattering cross-sections, general formulation 268 269
Scattering cross-sections, identical particles 280—281
Scattering cross-sections, inelastic scattering 263 265 269
Scattering cross-sections, neutron scattering 266—268
Scattering cross-sections, neutron-proton 277
Scattering cross-sections, partial waves 281—288
Scattering cross-sections, particle waves of high angular momentum 288—290
Scattering cross-sections, path integral formulation 265—268
Scattering cross-sections, phase shift analysis 281—288
Scattering cross-sections, shadow 268 290
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