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Beard D.B. Ч Quantum Mechanics
Beard D.B. Ч Quantum Mechanics

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Ќазвание: Quantum Mechanics

јвтор: Beard D.B.


This book was written with the aim of providing an alternative to the postulatory approach currently used in many introductory quantum mechanics courses. Thus the first chapters are designed to familiarize the reader with the mathematical treatment and particular properties of ordinary wave motion which apply also to particle motion and have crucial importance to the subsequent development of the subject. The close relation of quantum theory to physical optics is stressed, and by use of Feynman's derivation of quantum mechanics, the wave theory for particles is made to appear as inevitable and necessary as Huygens wave theory for light.

язык: en

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1970

 оличество страниц: 309

ƒобавлена в каталог: 16.04.2010

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ѕредметный указатель
Absorption, radiation      190Ч192
Absorption, radiation with ionization      203Ч205
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      254Ч260
Angular momentum, commutation relations      136Ч138
Angular momentum, eigenvalues      132Ч133 140
Angular momentum, light      194Ч195
Angular momentum, matrix representation      235Ч238
Angular momentum, operators      130Ч132
Angular wave functions in spherical coordinates      127Ч129
Antisymmetric spin state      246
Antisymmetric wave function      246
Antisymmetric wave function, first excited state of helium atom      221Ч222
Approximation, Born scattering cross-sections      269Ч279
Approximation, slowly varying potential (semiclassical)      110Ч117
Approximation, time dependent perturbation theory      184Ч198
Approximation, time independent perturbation theory      161Ч175
Approximation, variational method      179Ч182
Approximation, Wentzel Ч Kramers Ч Brillouin (WKB)      110Ч117
Associated Laguerre functions      148
Associated Legendre functions      127Ч129 134Ч136 139
Associated spherical harmonics      126Ч129
Atomic excitation by ion bombardment      188Ч190
Atomic excitation, radiative absorption      190Ч192
Atomic form factor      278 279
Average energy of mode of oscillation      8Ч12
Average value      68
Azimuthal angular wave function      127
Babinet's theorem      268
Balmer formula      148 149
Band theory of metals      99Ч106
Barrier penetration, square barrier      85Ч92
Barrier penetration, WKB approximation      121Ч123
Bessel function, one-half order      142Ч145
Bessel function, one-third order      113 114
Bessel function, spherical      142Ч145
Beta-decay, conservation of parity      252Ч254
BKW approximation      110Ч117 see
Bloch wave function      102Ч104
Bohr Ч Sommerfeld quantum conditions      117Ч120
Bohr, Niels, atomic orbits      46
Bohr, Niels, description of light diffraction      41
Bohr, Niels, frequency condition      187
Boltzmann constant      8
Born approximation      269Ч279
Bound particles in a square well      94Ч98
boundary conditions      4 12
Bra-vector      216Ч217
Bragg x-ray diffraction      46
Center of mass coordinates      78Ч81
Center of mass motion equation      80
Characteristic functions      13 see
Characteristic values      13 see
Chemical binding      208Ч209
Classical action      56
Classical path taken by particle or light ray      111
Clebsch Ч Gordon coefficients      254Ч260
Commutation relations      71Ч76
Commutation relations between coordinate and momentum      72
Commutation relations, angular momentum      136Ч138
Commutation relations, spin      243
Commutator      72
Commuting operators, diagonal representation      238Ч245
Complementary variables      16 34
Complete set      158 159
Compton effect      36Ч38
Compton wavelength      38
Continuity equation      77 78
Cosine series      17Ч19
Coulomb integrals      218 219
Coulomb integrals, hydrogen molecule      224Ч225
Coulomb potential, scattering cross-section      275 276
Currents, particles      77 78
Davisson Ч Germer experiment      45 46 49Ч52
de Broglie wavelength      46
Degeneracy in spherical harmonic oscillator      154
Degenerate perturbation theory      171Ч175
Degenerate perturbation theory, harmonic oscillators      213Ч216
Degenerate perturbation theory, helium atom, first excited state      218Ч222
Degenerate perturbation theory, hydrogen molecule      222Ч226
Delta-function, Dirac      21
Delta-function, Kronecker      17
Deuteron      97 98
Diagonal operators, commutation of      238
Diagonalization of an operator      234
Diffraction, electrons      45Ч46 49Ч52
Diffraction, light (interference of photons)      38Ч41 52Ч54
Diffraction, particles      45 46 54Ч58
Dipole transitions      192Ч196
Dirac delta-function      21
Dirac notation      216 217
Eckart Ч Bethe potential      118Ч120
Effective range      293Ч294 296
Eigenfunctions      13
Eigenvalues      13 67
Eigenvalues, angular momentum      132 133 140
Einstein A and B coefficients      198Ч200
Electromagnetic waves in a box      1Ч6 see
Electron, angular momentum operator      244Ч245
Electron, diffraction      45Ч52
Electron, emission from metals      122 123
Electron, interaction in atoms, general discussion      227Ч230
Electron, wave functions and energies in a metal      99Ч106
Emission of radiation      198Ч200
Energy levels, atomic      148
Energy levels, bound particle in a potential      111
Energy levels, degenerate perturbation theory      171Ч175
Energy levels, harmonic oscillator, linear      155
Energy levels, harmonic oscillator, spherical      153 154
Energy levels, hydrogen      148
Energy levels, nuclear potential      118Ч120 154
Energy levels, splitting due to mutual repulsion of electrons      178
Energy levels, splitting due to mutual repulsion of electrons, helium atom      217Ч222
Energy levels, splitting due to spin orbit force      176Ч178
Energy levels, square well, spherical      145
Energy operator      68
Exchange integrals      218 219
Exchange integrals, hydrogen molecule      224Ч225
Exchange operation      245Ч246
Excitation, atomic by ion bombardment      188Ч190
Excitation, atomic by radiation      190Ч192
Exclusion principle, Pauli      247
Expectation      68Ч70
Expectation of coordinates      68
Expectation of coordinates, time derivative      74 75
Expectation of operator      72
Expectation, energy      73
Expectation, momentum operator      69
Expectation, momentum operator, derivative      75
Expectation, time derivative      73 74
Expected value      68
Fermat's principle      111
Fermi level, Fermi energy      102
Fermi scattering length      288 296
Fine structure      175Ч178
Fine structure, hydrogen atom      176Ч178
Form factor, atomic      278 279
Fourier series      17Ч19
Fourier transform      20Ч26 271Ч273
Fourier transform, Gaussian distribution function      24Ч30
Franck and Hertz experiment      35 36
Frequency spread and time duration      23Ч26
Gaussian distribution, Fourier transform      20 30
Gaussian wave packet      29 30 65 66
Group velocity      28 65 66
Hamilton's principle function      56 111
Hamiltonian      69
Harmonic oscillator, coupled, classical      209Ч211
Harmonic oscillator, coupled, quantum mechanical      212Ч216
Harmonic oscillator, linear      155
Harmonic oscillator, selection rules      196 197
Harmonic oscillator, spherical      150Ч154
Heisenberg uncertainty principle      see "Uncertainty principle"
Heitler Ч London theory, calculation of the hydrogen molecule      222Ч226
Helium atom, first excited state      217Ч222
Helium atom, ground state, first order perturbation theory      164Ч168
Helium atom, ground state, variational method      181 182
Hermite polynomials      154
Hermitian operators      75 76
Hund's rule      248 249
Hydrogen atom      146Ч150
Hydrogen atom, fine structure      176Ч178
Hydrogen atom, selection rules      197 198
Hydrogen atom, wave functions      146 148
hydrogen molecule      222Ч226
Indices of refraction, particles and light      65
Induced emission      200
Interference of photons      38Ч41
j-j coupling      230
Ket-vector      217
Kronecker delta      17
Kronnig Ч Penney potential      102Ч106
L*S coupling      175Ч178 229 230
Lagrangian      56
Laguerre functions and polynomials      148
Legendre polynomials      see "Associated Legendre functions"
Lienard Ч Wiechart retarded potential      270Ч272
Light, angular momentum      194 195
Light, probability amplitude      52Ч54
Linear independence      171
London Ч Heitler theory of hydrogen molecule      222Ч226
Matrices, spin      242Ч245
Matrix representation, angular momentum      235Ч238
Matrix representation, operators on eigenfunctions      232Ч234 235
Maxwell Ч Boltzmann energy distribution      8
Maxwell's equations      2
Microscope experiment      41Ч43
Momentum operator      68 70
Momentum transfer      273
Mott scattering      280Ч281
Neutron-proton scattering cross-section      277
Newton's second law, quantum mechanical version      75
Normalization of wave functions      158
Nuclear potential      118Ч120
Nuclear potential, energy levels      117Ч120 154
Nuclear potential, wave functions in a harmonic oscillator potential      151Ч155
Nuclear potential, wave functions in a square well      141Ч145
Observables, physical      67Ч71 75 76
Octupole transition      195
Operation      12
Operator      12 67Ч71
Operator, angular momentum      130Ч132
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      158Ч161
Orthogonality of wave functions, degenerate      171Ч172
Orthogonalization of eigenfunctions belonging to a degenerate energy level      171 172
oscillators      see "Harmonic oscillators"
Oscillators, coupled, classical      209Ч212
Oscillators, coupled, quantum mechanical      212Ч216
Parity      249Ч254
Parity of eigenfunctions      232
Parity, angular momentum and spin      250
Parity, conservation      250Ч254
Parity, conservation, beta decay      252Ч254
Partial waves, scattering theory      281Ч288
Particle, current density      77 78
Particle, probability amplitudes      54Ч58
Particle, wave characteristics of      41Ч43
Particle, wave packet      65 66
Particle, waves      64Ч66
Pauli exclusion principle      247
Pauli theory of spin (spin matrices)      242Ч245
Penetration through a barrier, square barrier      85Ч92
Penetration through a barrier, WKB approximation      121Ч123
Perturbation theory, degenerate      171Ч175
Perturbation theory, degenerate, harmonic oscillators      213Ч216
Perturbation theory, degenerate, helium atom, first excited state      218Ч222
Perturbation theory, time dependent, first order      184Ч187
Perturbation theory, time dependent, second order      201Ч203
Perturbation theory, time independent, first order      161Ч164
Perturbation theory, time independent, second order      169Ч170
phase velocity      28
Photolectric effect      35 45
photons      33Ч40
Photons, diffraction and interference      38Ч41
Photons, probability amplitude      52Ч54
Planck black body distribution      9 11
Planck's constant      10 11
Plane wave in a string      299Ч301
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      52Ч54
Probability amplitude, particle      54Ч58
Probability in volume of momentum space      71
Pseudoscalars      252Ч253
Pseudovectors      252
Quadrupole transition      195
Quanta      33Ч40
Radiation, Energy density      8Ч12
Radiation, number of modes of vibration      6Ч7
Radiation, pressure      36 37
Radiation, transitions      190Ч192
Ramsauer effect      93 94
Rayleigh Ч Jean's law      9
Reduced mass      79
Reduced mass, effect in scattering cross-sections      274
Refraction index      65
Relative motion equation      80
Resonance classical      207 208 211 212
Resonance integrals      218 219 224 225
Resonance, energy      220Ч221
Resonance, helium atom, first excited state      218Ч222
Resonance, quantum mechanical oscillators      212Ч216
Rigid rotator      139 140
Russell Ч Saunders coupling      230 249
Rutherford's experiment      44
Scattering cross-sections      263Ч265
Scattering cross-sections, alpha particles      279
Scattering cross-sections, atomic by the Born approximation      277Ч279
Scattering cross-sections, Born approximation      269Ч279
Scattering cross-sections, classical limit      290
Scattering cross-sections, constant potential by Born approximation      279
Scattering cross-sections, Coulomb potential by Born approximation      275Ч279
Scattering cross-sections, differential scattering cross-sections      264Ч265
Scattering cross-sections, effective range theory      291Ч296
Scattering cross-sections, Fermi scattering length      288 296
Scattering cross-sections, general formulation      268 269
Scattering cross-sections, identical particles      280Ч281
Scattering cross-sections, inelastic scattering      263 265 269
Scattering cross-sections, neutron scattering      266Ч268
Scattering cross-sections, neutron-proton      277
Scattering cross-sections, partial waves      281Ч288
Scattering cross-sections, particle waves of high angular momentum      288Ч290
Scattering cross-sections, path integral formulation      265Ч268
Scattering cross-sections, phase shift analysis      281Ч288
Scattering cross-sections, Scattering cross-sections, billiard ball collision by Born approximation      279
Scattering cross-sections, shadow      268 290
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