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| Авторизация |
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| Поиск по указателям |
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| Prugovecki E. — Quantum Mechanics in Hilbert Space |
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| Предметный указатель |
Physical equivalence 293
Physical interpretation see “Measurement theory
Planck constant 46
Plane waves, advanced distorted 495
Plane waves, distorted 494
Plane waves, free 491
Plane waves, incoming distorted 495
Plane waves, outgoing distorted 495
Plane waves, retarded distorted see “Plane waves outgoing
Potential, central 149
Potential, long-range 514
Potential, spherically symmetric 149
Pre-Hilbert space 18
Principle of indistinguishability of identical particles 307
probability 46
Probability, amptitude see “Transition amplitude”
Probability, current 410 411
Probability, frequency interpretation 47
Projector 197
Quantum number, azimuthal 168
Quantum number, magnetic 168
Quantum number, principal 168
Quotient space 138
R operator 511
Radon — Nykodim theoreom 269
Rellich’s theorem 366
Resolution of identity 235
Resolvent equations, first 478
Resolvent equations, second 478
Resolvent of operators 475
Resolvent set 475
Riemann — Lebesgue lemma 216
Riemann — Stieltjes sums 464
Riesz theorem 184
Riesz — Fischer theorem 105
Ring, boolean 66
Rodrigues’ formula 152
Rollnik class 545
Rollnik norm 545
S matrix 512 (see also “Scattering matrix”)
S matrix, partial-wave 497
S operator 423 438
S operator for multichannel scattering 607 613
S operator, perturbation expansion of 450
S operator, unitarity of 442
Scalar product see “Inner product”
Scattering, amplitude 494 553 556
Scattering, elastic 597
Scattering, experiments 416 425
Scattering, inelastic 598
Scattering, matrix 512
Scattering, operator see “S operator”
Scattering, state 421
Scattering, superoperator 487
Scattering, theory, stationary 458
Scattering, theory, three-body 622
Scattering, theory, time dependent 438
Scattering, theory, time independent see “Scattering theory stationary”
Schmidt procedure see “Vectors”
Schroedinger equation 3 46 48 122 332
Schroedinger operator 355
Schroedinger operator, essential self-adjointness of 358 368
Schroedinger operator, form 122
Schroedinger operator, n-body 536
Schroedinger picture 291
Schwarz — Cauchy inequality 19 20
Self-adjoint operators 192
Self-adjoint operators, commuting 258 259 261
Self-adjoint operators, spectral measure of 250
Sequence of operators see “Operators sequences”
Sequence, Cauchy 26
Sequence, contracting see “Sequence monotonically
Sequence, convergence in mean 105
Sequence, expanding see “Sequence monotonically
Sequence, fundamental 104 (see also “Sequence Cauchy
Sequence, monotonically decreasing 63
Sequence, monotonically increasing 63 209
Sesquilinear forms see “Bilinear form”
Set function 58
Set function, continuous 68
Set function, measurable 80
Set function, monotone 79
Set function, subtractive 79
Sets, additive class of see “Ring Boolean”
Sets, Borel measurable 80
Sets, closed 27
Sets, Lebesgue measurable 80
Sets, measurable 65 71 74
Sets, monotone class of 63
Sets, partially ordered 203
Shift operator 213
Spectral decomposition of operators 242 252
Spectral family see “Spectral function”
Spectral function 235
Spectral integrals 483
| Spectral measure 231
Spectral representation space of operators 315
Spectrum of operators, absolutely continuous 438
Spectrum of operators, continuous 253 475
Spectrum of operators, discrete 537
Spectrum of operators, essential 537
Spectrum of operators, point 49 227 253 475
Spectrum of operators, residual 475
Spectrum of operators, simple 315 447
Spectrum of operators, singularly continuous 552
Spherical wave, outgoing free 496
Spin, measurement of 9
Spin, Stern — Gerlach experiment 9
State vectors 301
States 2
Statistical operator 269
Stern — Gerlach experiment see “Spin”
Stochastic phase space 410
Stochastic value 410
Stone’s theorem 335
Subspaces, orthogonal complements of 199
Subspaces, orthogonal sums of 199 200
Super selection rules 301 302
Superoperator 398
T matrix 508 620 matrix”)
Tensor product 303
Tensor product, algebraic 141
Tensor product, antisymmetric 306
Tensor product, Hilbert 144
Tensor product, symmetric 306
Threshold 598
Time evolution 287 292
Tonelli’s Theorem 98
Trace of an operator 380
Trace of an operator, class 380
Transform, Cayley 219 223
Transform, Fourier 218
Transform, Fourier — Plancherel 219 224
Transformations of vector spaces 172 (see also “Operators”)
Transformations, antilinear 172
Transformations, bounded 178
Transformations, continuous 178
Transformations, isometric 212
Transformations, linear 172
Transformations, semilinear see “Transformations antilinear”
Transformations, unitary 212
Transformer 398
Transition, amplitude 472
Transition, matrix 506 510
Transition, operator 423 474 510
Transition, probability 268 472
Transition, superoperator 488
Translation 576
Trotter’s product formula 585
Unitary equivalence 332 (see also “Isomorphism of Euclidean spaces”)
Unitary operator 212
Unitary space see “Euclidean spaces”
Vector basis 15
Vector spaces 11 36
Vector spaces, algebraic tensor products of 141
Vector spaces, conjugate see “Vector spaces dual”
Vector spaces, dimension of 14
Vector spaces, dual 183
Vector spaces, functional on 182
Vector spaces, inner product see “Euclidean spaces”
Vector spaces, isomorphism of 16
Vector subspace 16
Vectors, bra 186 190
Vectors, ket 186 190
Vectors, linearly independent 14
Vectors, normalization of 21
Vectors, orthogonal 21
Vectors, orthogonal system of 21
Vectors, orthonormalization procedure of Schmidt (or Gram — Schmidt) 22
Vectors, span of 15 36
von Neumann’s equation 396
von Neumann’s theorem 342
Wave function 45 120
Wave operators, channel 603
Wave operators, complete 552
Wave operators, existence of 438
Wave operators, incoming 423
Wave operators, intertwining properties of 439 603
Wave operators, modified 514
Wave operators, outgoing 423
Wave operators, renormalized 514
Wave packet, evanescence of 596
Wave superoperators 487
Wave, advanced distorted see “Wave incoming
Wave, free 491 496
Wave, incoming distorted 495 496
Wave, outgoing distorted 495 496
Wave, retarded distorted see “Wave outgoing
Weierstrass approximation theorem 157
Weyl relations 333
Yukawa interaction 365
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