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| Kemble E. C. — The fundamental principles of quantum mechanics |
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| Предметный указатель |
Action function 25 44
Action integral 8 25 560
Action variable 375
Addition of states 201
Adiabatic theorem 431 432
Adjoint manifold of operator 276
Adjoint matrix 350
Adjoint operator, first definition of 122n
Adjoint operator, second definition of 203 512
Alkali spectra, energy levels of 474—481
Alkali spectra, theory of fine structure of 503—507 519—522
Alpha particles, emission of 179 187—192
Analytic function 140
Analyticity of wave functions 18 198 200
Angular momenta, combination of 495 498 537—540
Angular momentum of electron spm 500 503 504 510—519 529
Angular momentum of system of particles 224 227—234 292 293
Angular momentum, internal 228
Angular momentum, resultant of spin and orbital 498 504 520
Angular-momentum operators 224—234 292 293 314—317
Angular-momentum quantum number 151 234 493
Antisymmetric wave functions 337 531 533—536
Antisymmetrizer 535 536
Antisymmetrizing operator 9 338 529 534 535
Assemblages, canonical 434 446
Assemblages, chaotic 438
Assemblages, concrete 55 319
Assemblages, Gibbsian 53—55 329 433—448
Assemblages, mixed case 54 320
Assemblages, pure case 320
Asymptotic agreement of classical and quantum theories 51 229 230 302
Atomic energy levels, classification of 493 494 538 539
Atomic model of Bohr, idealized 474
Atomic units 420
Atoms, complex in problem A approximation 528
Atoms, complex in problem B approximation 528 555
Atoms, complex in problem C approximation 528
Atoms, complex with many electrons 474—556
Atoms, complex, perturbation theory of 484—488 526—528
Auger effect 195 213 214
Azimuthal quantum number 151
Bessel’s inequality 136
Binomial coefficients 586
Bohr theory 91 108 157 178
Bohr theory, postulates of 374
Boundary and continuity conditions 78 197—201
Boundary conditions, linear homogeneous 125 130
Boundary conditions, physical 126 153
Boundary conditions, singular-point 125—128 130 131 153
Brillouin — Wentzel — Kramers method 46 90—112 152 155 157 158 168 182 572—578 587
Brillouin — Wentzel — Kramers method, higher approximations of 107
Brillouin — Wentzel — Kramers method, modification of, for radial motion 107 108 155
Broadened energy levels 181 183 195
Calculus of variations 130 557—563
Canonical assemblage 434 446
Canonical equations (see Hamilton’s canonical equations of motion)
Canonical Heisenberg matrices 367
Canonical Schrodinger matrices 369
Canonical transformation 247 355 357 358
Central-field approximation 485 526 541—543 548
Characteristic values (see Eigenvalues)
Classical local momentum 9 20 69 81
Classical orbits 331—334
Closed shells 536 537
Commutation and simultaneous measurements 334
Commutation rules for anguiar-momentum components 292 293
Commutation rules for conjugate dynamical variables 282
Commuting operators 281—286
Commuting set of dynamical variables, normal 286 287
Commuting set of observables, normal 339
Complete set of mutually compatible operators 254
Complete set of normally commuting dynamical variables 287
Complete set of normally commuting observables 339 531 532
Completeness of system of functions 119 120 136 137 144 149 150 216 253 254
Completeness of system of functions with continuous spectrum 165 171 172
Completeness, modified form of 137
Complex eigenvalues of non-Hermitian operators 242n
Complex eigenvalues of weakly quantized states 192—194
Configuration space 21 115
Configuration space with electron-spin coordinates 510 512 523 524
Configuration, electronic 526
Conjugate dynamical variables 26 74 282 293—299
Conjugate dynamical variables, measurement of 334
Conjugate dynamical variables, spectra of 299
Connection formulas 94 100—103 111 183
Conservatio of an arbitrary dynamical variable 290
Conservatio of electricity 222
Conservatio of energy 288
Continuant 407
Continuous spectrum 85
Continuous spectrum and perturbation theory 394
Continuous spectrum normalization of 164 169 170 176—178
Continuous spectrum of many-particle problem 215—217
Continuous spectrum, elimination of 163
Continuous spectrum, limit of 211 212
Continuous-spectrum eigenfunctions not quadratically integrable 226
Convergence of perturbation theory 382
Convergence, mean-square 138 217
Coordinate system in quantum mechanics 236
Corpuscular nature of matter 87n
Corpuscular theory of light 2 3
Correspondence principle of Bohr theory 3 367 375 451
Coupling of individual electrons 537—540
Current of probability 189
Current, electric 222
Current, mass 31 32 110 222 577
Degeneracy 147 150 217 218 311—317
Degeneracy, accidental 312
Degeneracy, continuous-spectrum 312
Degeneracy, Coulomb 312
Degeneracy, physical vs. mathematical 531
Degeneracy, removal of, for set of simultaneous eigenvalues 287
Degeneracy, symmetry 312
Density function, or density factor 123 124 128 164 239 268
Determinant of matrix 350
Determinant, functional or Jacobian 64 238 248 269 295
Determinism and indeterminism 6 7 76
Diagonal sum method 555
Diatomic molecule, dumbbell model of 155 386 419
Diatomic molecule, fixed nuclei problem of 419—426
Diatomic molecule, perturbation theory of 386
Differentiation of functions of operators 300
Diffraction of electrons 14 70
Dirac function 267
Dirac notation for probability amplitudes 268
Dualistic nature of light 3—7
Dualistic nature of matter 3 52
Dynamical variables, conjugate 26 293—300
Dynamical variables, mathematical definition of 264 276
Dynamical variables, non — Hermitian 275
Dynamical variables, operational definition of 318
Dynamical variables, simultaneously measurable 257
Dynamical variables, symmetric 337
Dynamical variables, unitary 275
Eigendifferentials 164 169 170 216 252
Eigenfunctions 80
Eigenfunctions of general Hermitian operator 252
Eigenfunctions, simultaneous 252 284 285
Eigenvalue-eigenfunction problem 80
Eigenvalue-eigenfunction problem as a principal-axis transformation 362 372 373
Eigenvalue-eigenfunction problem, matrix form of 359
Eigenvalue-eigenfunction problem, v.Neumann form of 263
Eigenvalue-eigenfunction problem, variational forms of 130—132 206 207 578—582
Eigenvalues 80
Eigenvalues of Hermitian operator (definition) 251
Eigenvalues of unitary operator 275 276
Eigenvalues of variational pfoblem 131
Eigenvalues, complex, of non-Hermitian operator 24n 275
Eigenvalues, complex, of weakly quantized states 192—194
Eigenvalues, reality of 123 128 206 275
| Eigenvectors, j 369 391
Electron spin, classical theory of 500 503 524
Electron spin, Pauli theory of 510—522 523
Electron-spin hypothesis 491 492
Electron-spin matrices 512—519
Electron-spin operators 512—519
Electronic configuration 526
Electronic configuration, terms originating in an 537—540
Energy levels, broadened 181 183 195
Energy levels, classification of atomic 493 494 538 539
Energy levels, of alkali atoms 474—481
Energy levels, splitting of, by perturbations 388
Energy operators 234—240 (see also Hamiltonian operator)
Energy variation when Hamiltonian depends 289
Energy, measurement of 328—331 344 347
Equation of continuity 31
Equivalent electrons 536 539 540
Euler’s angles 231
Euler’s equation 557—559
Even and odd states 314 531 541
Everywhere-dense manifold 201
Exchange energy 553 554
Existence of eigenvalues of one-dimensional oscillator 84
Existence of solutions, of many-particle problem 196 208 214
Existence of system of simultaneous eigenfunctions 284 285
Existence of the Sturm — Liouville problem 128 129
Existence of v. Neumann eigenvalue problem 278
Expansion in series of functions 113 120 135 226 234
Expansion, series-integral 164 176 215—217 255
Expansions with mean-square convergence 138 217 242
expectation value (see Mean value statistical)
Extremals 131 559
Fermat’s principle 7—10 12 20 22 47
Fine structure of alkali spectra, theory of 503—507
Fine structure of optical atomic spectra 491—495
Fischer — Riesz theorem 259 262 274
Fourier analysis 12 62 67
Fourier integral theorem 36 65 162 173
Fourier transform 36 221
Function space 119 (see also Hilbert space)
Functions not quadratically integrable 226
Functions of a normal set of commuting dynamical variables 286
Functions of bounded variation 566
Functions of class A 79 131 153
Functions of class B 80 86 162
Functions of class D 197—201
Functions of non-commuting linear operators 300
Functions, of a single operator 279
Functions, physically admissible 17 79 131 197 201 524
Functions, with electron-spin coordinates 524
Fundamental equation (see Indicial equation)
Geiger — Nuttall law 188
Gibbsian assemblage of independent systems 53—55 329 433—448
Gibbsian canonical assemblage 434 446
Group of the Schrodinger equation 310
Group velocity 10—13 20 39 42 49
Group, permutation 309 529
Group, rotatipn-reflection 308 529 532
gyromagnetic ratio 501
Hamilton — Jacobi equation 9 24 25 43 44
Hamilton's canonical equations of matrix form 367
Hamilton's canonical equations of motion, classical form of 22 24 293
Hamilton's canonical, operator form of 301 302
Hamilton's principle 559 560
Hamiltonian function, classical 23
Hamiltonian operator 24 28
Hamiltonian operator for complex atoms with spin 524—526
Hamiltonian operator, transformation of 237—240
Hartree self-consistent field 477 551
Heisenberg Inequality 73 222
Heisenberg matrices 367
Heisenberg uncertainty principle 72—77 192 222
Helium atom 209—212 547—553
Hermitian character of Hamiltonian 202—206 452
Hermitian domain 203
Hermitian manifold 210 251 263
Hermitian manifold of type Dy 251
Hermitian matrix 350
Hermitian operator 203 251 512 524
Hermitian orthogonal functions 90
Hermitian polynomials 90
Hilbert space 114 119n 120
Huygens’ principle 45 467
hydrogen molecule 419—426 552
Hydrogenic atom 157—161
Hydrogenic atom in electric field 403—408
Hydrogenic atom in magnetic field 398—403
Hydrogenic atom, relativistic theory of 507—509
Hydrogenic states of atoms 478
Identical particles 335—339
Identity of macroscopic bodies 340
Indicial equation 141 143 153
Integrals of the motion 291 311—313 396—398 528—533
Interchange operators or transpositions 308
Intersystem combination lines 527
Invariance with respect to substitution 303
Invariance, gauge 29
Jacobi polynomials 234 594 595
Jacobian determinant 64 238 248 269 295
Kronecker symbol 90
L complex 316 539
Lagrangian function 23n 293 560
Laguerre orthogonal functions 585—587
Laguerre polynomials 160 585
Lande magnetic core theory 498 499
Laporte rule 540 541
Larmor precession 400 401
Least action 7—10 12 20 560—562
Least time (see Fermat’s principle)
Legendre functions, associated 149 150 584
Legendre polynomials 143—145 583
Linear independence 117n
Linear manifold 201
Macroscopic bodies, identity of 340
Macroscopic bodies, trajectories of 331—334
Magnitude of a function 116
Matrices 348—474
Matrices with continuous elements 363—366
Matrices, Heisenberg 367
Matrices, Heisenberg canonical 367
Matrices, Schrodinger 367
Matrices, Schrodinger canonical 369
Matrices, similar 348
Matrix addition 348
Matrix form of eigenvalue-eigenfunction problem 359
Matrix multiplication 349
Matrix of a linear transformation 101 355
Matrix of an operator 352
Matrix transformation, canonical 355 357 358
Matrix, adjoint 350
Matrix, determinant of 350
Matrix, diagonal 284 349
Matrix, Hermitian, or self-adjoint 350
Matrix, ordered diagonal 349
Matrix, reciprocal 349
Matrix, step 351 390
Matrix, unit 349
Maximum-minimum principle 216
Mean value for a mixture 320
Mean value of a coordinate 50 219 220 270
Mean value of angular-momentum components 229 230
Mean value of arbitrary dynamical variable 242 243 258
Mean value of energy 234—236
Mean value of linear-momentum components 221
Mean value, statistical 72
Measurements 75 318—347
Measurements and identical particles 335—340
Measurements as correlations 342 343
Measurements individual 318
Measurements of energy 328—331 344 347
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