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Kemble E. C. — The fundamental principles of quantum mechanics
Kemble E. C. — The fundamental principles of quantum mechanics

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Название: The fundamental principles of quantum mechanics

Автор: Kemble E. C.

Аннотация:

This volume was originally intended to be an expansion of a summary of the elements of quantum mechanics written some years ago for the Reviews of Modern Physics by the author in collaboration with Professor E. L. Hill. The point of view is essentially the same as in the summary, but as the present work has grown in my hands it has lost most of its resemblance to the initial pattern.
The method of approach was dictated by the desire to meet the needs of graduate students of physics.
Author has borrowed freely from other books and am particularly indebted to those of von Neumann, Dirac, and of Born and Jordan.
It is a pleasure to thank my colleagues and former colleagues, Dr. Eugene Feenberg, Dr. W. H. Furry, Professor J. C. Slater, and Professor J. H. Van Vleck for invaluable suggestions and generous assistance.

Edwin C. Kemble


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1937

Количество страниц: 611

Добавлена в каталог: 26.04.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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      151 224—234 314 317
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
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