Page 359 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics

350 Index

Parseval's theorem 10, 18, 35, 41, 288±9, 291 for harmonic oscillator 110, 147±8, 162, 320±3
particle in a box 48±52, 64, 91, 104±5, 230 for orbital angular momentum 323±6
energy levels 50, 62±3 for radial equation 326±8
perturbed 261±2 Slater determinant 221±2
three-dimensional 61±3, 226 Sommerfeld, A. 226
and variation method 234±5 spherical harmonics 139±47, 161, 175, 177, 192,
wave functions 50±2, 62 274
Paschen series 156, 188±9 spin angular momentum 85, 194±207
Pauli, W. 195±6, 221 of bosons 197±8, 217±18, 221±3, 229±30
Pauli exclusion principle 221±2, 225, 227 discovery of 194±6
Pauli spin matrices 200±1, 207 eigenfunctions 197±9
permutation operators 212±16, 219±21 eigenvalues 197, 199
perturbation theory 239±58, 261±2 of electron 29, 32±4, 85, 190, 194±6, 201±6,
degenerate 248±56 223±4
®rst-order 240±3, 245, 250±4, 257±8, 261 of fermions 197±8, 217±18, 221±9, 231
applied to harmonic oscillator 246±8 gyromagnetic ratio 196
applied to helium atom 257±8 ladder operators 197, 199
applied to hydrogen atom 262 operators 196±7, 199, 202±6
applied to hydrogen atom in electric ®eld 254±6 singlet and triplet states 224
applied to a molecule 265±6, 276±9 spin one-half 198±201
non-degenerate 239±45 see also Pauli spin matrices
related to variation method 245 spinor 199
second-order 240, 243±5, 261 spin±orbit coupling 201±6, 262
applied to spin±orbit coupling 262 spring constant 107
Pfund series 188±9 square pulse distribution 12±13, 15, 35
phase velocity, see wave packet Stark effect in atomic hydrogen 254±6, 260±1
photon 1, 18±19, 24±6, 30±2, 187 state function 30, 38, 40, 85±6
spin of 217 see also wave function
Planck, M. 18 stationary state 47±8, 52, 59, 93±4
Planck relation 18, 157, 187 Stern, O. 19, 26
plane wave 2±9, 11, 22, 40 Stern±Gerlach experiment 26±9, 32±4, 195
postulates of quantum mechanics 85±94, 196, 217 symmetric wave function, see wave function
principle quantum number, de®ned 175
probability density, see wave function ± and
Thomas precession 202
probabilities
Thomson, G. P. 19
transmission coef®cient, see tunneling
radial distribution function 181, 184±6, 192 tunneling 53±7, 64
radiation, absorption and emission of 187
raising operators, see ladder operators
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Rayleigh±Schrodinger perturbation theory, see Uhlenbeck, G. E. 194±6
perturbation theory uncertainty principle, see Heisenberg uncertainty
reduced mass 149, 158, 175, 188, 270±1 principle
re¯ection coef®cient, see tunneling uncertainty relation, see wave packet ± uncertainty
rigid rotor 148±51, 274±6, 278 relation
rotational constant 150, 275 Urey, H. 190
Rydberg constant 156±7, 188, 190, 193
Rydberg potential 279±80 variation method 232±9, 260±1
excited state energies 236±7
Schmidt orthogonalization 72±3, 104 ground state eigenfunctions 234
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Schrodinger, E. 1, 20, 37 ground state energy 232±4
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Schrodinger equation applied to harmonic oscillator 235±6
for harmonic oscillator 109, 126 applied to helium atom 259±60
for hydrogen-like atom 159±61 applied to hydrogen atom in electric ®eld 260±1
for a molecule 264±5 linear variation function 237±9, 261
for particle in a box 48, 61 applied to particle in a box 234±5
time-dependent 37, 59, 85, 92±4 related to perturbation theory 245
time-independent 47, 59, 93, 96±7 variation theorem 232±3, 236
Schwarz's inequality 46, 284 vibration
secular determinant 78, 239, 251±2, 255 of molecular bonds 106
selection rules 192 see also harmonic oscillator
series solution method 318±20 virial theorem 187, 192