Page 357 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics

348 Index

Ehrenfest theorems 43±5, 59±60, 99, 105 gaussian distribution 10±11, 15, 17±18, 21, 34±5,
eigenfunctions 67±75, 80±3, 85, 87, 96, 104 102
completeness of 75±7 Gerlach, W. 26
expansions in 75±7, 84, 88±91, 94, 198 see also Stern±Gerlach experiment
for generalized angular momentum 133±4 Goudsmit, S. 194±6
normalization 38±41, 47, 51, 58, 69, 86, 98 group velocity, see wave packet
orthogonality 51, 69, 71±4, 80, 211, 215, 217 gyromagnetic ratio 196
scalar product of 68±9
simultaneous 77±9
for spin angular momentum 197±9
well-behaved, de®ned 68, 162 Hamiltonian operator 85, 87, 93, 95±6
see also wave function de®ned 47
eigenket, see eigenfunctions, wave function for harmonic oscillator 109
eigenvalues 67±8, 71, 85, 87±90, 104 for helium atom 224, 256
for generalized angular momentum 133±4, 137 for hydrogen-like atom 159, 161, 191, 260
for orbital angular momentum 138, 140 for a molecule 263±4
for spin angular momentum 197, 199 for multi-particle system 60
see also degeneracy, energy levels for non-interacting particles 220
eigenvector, see eigenfunctions, wave function perturbed 240, 246, 248
Einstein, A. 18±19, 229 for rigid rotor 150
electron spin 29, 32±4, 85, 190, 194±6, 201±6, for spin±orbit coupling 202±3, 206
223±4 symmetry of 209, 212, 216
electron volt, de®ned 168 three-dimensional 59
emission of radiation 187 harmonic oscillator 106±29
energy levels classical 106±9, 128
for diatomic molecule 276±9 energy levels 113±14, 127±9, 323
for harmonic oscillator 113±14, 127±9, 323 Hamiltonian operator 109
for hydrogen-like atom 168, 175±6, 191±2, isotropic 127±9
254±6, 261±2, 328 ladder operators 110, 128
for particle in a box 50, 62±3 linear 109±21
for rigid rotor 150 matrix elements 121±5, 129
see also perturbation theory, variation method applied to nuclear motion 275±6
Estermann, I. 19 perturbed 246±8
È
exchange forces 223 Schrodinger equation 109, 126
three-dimensional 125±9
exchange operators 210±11, 213±16, 230
and variation method 235±6
exclusion principle, see Pauli exclusion principle
wave functions 114±21, 127, 320±3
expectation values 41±5, 47±8, 59, 85, 87±91,
104±5 zero-point energy 113
for harmonic oscillator 128 see also anharmonic oscillator
for hydrogen-like atom 181, 184, 186±7, 192±3, Heisenberg, W. 34
329±30 Heisenberg uncertainty principle 21±3, 29, 45±6,
for particle in a box 104 99±105, 155
time dependence 97±8 for harmonic oscillator 125
for time and energy 22, 31, 103±4
and zero-point energy 50
see also wave packet ± uncertainty relation
Fermi, E. 19 helium
Fermi energy in free-electron model 227±9 atom 217±18, 223±5, 256±60
fermion 197±8, 217±18, 221±9, 231 ion 193
®ne structure constant 203 liquid 218, 230
force constant for vibration 106, 273 Hellmann±Feynman theorem 96±7, 186, 192
Fourier series 4, 285±9 Hermite polynomials 117±18, 296±300, 323
Fourier transform 8, 10, 14±15, 22, 37, 40, 42, 58, hermitian operator, see operator
102, 289±91, 294 Hilbert space 80
free-electron gas 226±9, 231 Hooke's law 107
frequency Humphreys series 188±9
angular, de®ned 3 hydrogen-like atom 156±7, 160±93
of vibration, de®ned 107 atomic orbitals 175±82, 254±6
of a wave, de®ned 2 Bohr model 156±7, 168, 175
see also harmonic oscillator, wave motion Bohr radius 175, 184
Frisch, R. 19 in electric ®eld 254±6, 260±1
Frobenius method, see series solution method energy continuum 174±5