Page 358 - PRINCIPLES OF QUANTUM MECHANICS as Applied to Chemistry and Chemical Physics

Index 349

energy levels 168, 175±6, 191±2, 254±6, 261±2, magneton, Bohr, de®ned 152
328 Marshall, L. 19
expectation values 181, 184, 186±7, 192±3, matrices
329±30 properties of 331±40
Hamiltonian operator 159, 161, 191, 260 spin 200±1, 207
ionization potential 169 matrix elements 81
ladder operators 163 of harmonic oscillator 121±5, 129
in a magnetic ®eld 190±2 metallic crystal 226, 228±9, 231
perturbed 206, 254±6, 262 molecular spectra 279
quantum numbers 175±6 molecular structure 263±80
radial distribution function 181, 184±6, 192 adiabatic approximation 268±9, 272±3
radial functions 161±75, 181, 183, 185, 326±8 Born±Huang treatment 266±9
Rydberg constant 156±7, 188, 190, 193 Born±Oppenheimer approximation 264±6,
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Schrodinger equation 159±61 268±9, 273
spectra 156±7, 187±90, 192±3 diatomic molecule 269±80
spin±orbit coupling 201±6, 262 nuclear wave function 265±8, 273±4, 276
wave functions 161, 175 moment of inertia 149, 278
momentum operator 43±4, 58, 70, 86
identical particles 85, 208±17, 221 momentum space wave function, see wave function
de®nition 208 ± in momentum space
non-interacting 220±3, 226±30 Morse potential 279±80
and symmetry of wave functions 209±11, 230
see also boson, exchange operators, fermion, normalized functions 38±41, 47, 51, 58, 69, 86, 98
permutation operators nuclear motion, see molecular structure
ionization potential
for hydrogen 169 operator
for lithium ion 193 adjoint 82±3, 163
exchange 210±11, 213±16, 230
ket vector, de®ned 80 for generalized angular momentum 132±4, 155
see also eigenfunctions hermitian 69±75, 77±87, 104
linear 65±8, 85, 104
ladder operators 106 for momentum 43±4, 58, 70, 86
for generalized angular momentum 134±7, 155 for orbital angular momentum 131±2, 139,
for harmonic oscillator 110, 128 149±50, 155, 160±1, 202±6
for hydrogen-like atom 163 parity 94±6, 253
for orbital angular momentum 140±1 permutation 212±16, 219±21
for spin angular momentum 197, 199 projection 83±4
Laguerre polynomials 310±12 self-adjoint, see operator ± hermitian
associated 171±4, 192, 312±17, 328 for spin angular momentum 196±7, 199, 202±6
Larmor frequency 153±4 see also Hamiltonian operator, ladder operators
Legendre polynomials 301±4 Oppenheimer, J. R. 265
associated 147, 304±9, 325±6 orbital angular momentum 130±2, 138±46, 155
linear variation function 237±9, 261 classical 130±1
linear vector space 337±9 eigenvalues 138, 140
lithium ladder operators 140±1
atom 230 and magnetic moment 151±5, 190, 201
ion 193 operators 131±2, 139, 149±50, 155, 160±1,
lowering operators, see ladder operators 202±6
Lyman series 156, 188±9 operators in spherical polar coordinates 138±40
spin±orbit coupling 201±6, 262
magnetic moment wave functions 138±47, 323±6
of electron spin 26±9, 32±3, 190, 196, 201±2, orbitals, atomic, see atomic orbitals
204 orthogonal functions 51, 69, 71±4, 80, 211, 215,
of hydrogen atom 190±2 217
orbital 151±5, 190, 201 expansions in terms of 75±7, 84, 88±91, 94, 198
of particles with spin 196 orthonormal functions, de®ned 51±2, 69
magnetic interactions oscillator, see harmonic oscillator
with atoms 153±5, 190±2 overlap integral 237
within an atom 201±2
see also Stern±Gerlach experiment parity 95, 192
magnetic quantum number, de®ned 176, 191 operator 94±6, 253