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| Pugovecki E. — Quantum mechanics in hilbert space |
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| Предметный указатель |
Accumulation point 27
Additive class see Algebra Boolean
Akhiezer, N.I. 256 309 595
Algebra, associative 174
Algebra, boolean 58 60
Algebra, commutative 175
Algebra, generated by observables 276
Antoine, J.-P. 186 595
Asymptotic condition, physical 432 434
Asymptotic states in classical mechanics 393
Asymptotic states in multichannel scattering 578
Asymptotic states in potential scattering 541
Asymptotic states of interaction picture 451
Asymptotic states, incoming 394 395
Asymptotic states, outgoing 394 395
Axioms 2
Axioms for spin and statistics 309
Banach space 30
Bateman, H. 166 595
Bauer's formula 570
Belinfante, J.G. 594 595
Berezanskii, Yu. M. 594 595
Bessel's inequality 38
Bilinear form 137
Birkhoff, G. 56 595
Birman, M.S. 594 595
Borel set 62
Born approximations 533
Born, M. 46 260 595
Bose — Einstein statistics 307
Bosons 353
Bound state 49
Bound state, energy eigenvalues of 49
Bounded variation 442
Brascamp, H.J. 594 598
Butkov, E. 468 595 639
Canonical commutation relations 329
Canonical commutation relations, irreducible representation 341
Canonical commutation relations, reducible representation 341
Canonical commutation relations, representation of 331
Canonical form see Spectral representation space of operators
Channel, arrangement 574
Channel, concept of 574
Channel, energy 575
Channel, incoming 575
Channel, outgoing 575
Characteristic function 81
Characteristic subspace 227
Characteristic value see Eigenvalue
Characteristic vector see Eigenvector
Closed graph theorem 210
Closure 27
Cluster poin see Accumulation point
Collision, rearrangement 576
Confluent hypergeometric equation 165
Confluent hypergeometric function 165
Copenhagen school see Measurement
Correspondence rule 3 259
Courant, R. 595
Cross section, differential 403
Cross section, total 403
de Alfaro, V. 572 594 595
Decomposition of identity see Spectral function
Deficiency index 223
Deficiency subspace 223
Dennery, P. 56 595
Diffraction effect 7
Dirac delta function 478
Dirac, P.A.M. 1 18 311 595
Direct sum of Euclidean spaces 133
Distance function see Metric
Dixmier, J. 171 595
Dollard, J.D. 428 593 595
Dynamical law 2
Eigenfunction 462
Eigennumber 462
Eigenvalue 48 226
Eigenvalue equation 47
Eigenvalue, degenerate 49
Eigenvalue, multiplicity of 500
Eigenvalue, nondegenerate 49
Eigenvector 226
Energy shell 476
Ensemble, state of 386
Equal a priori probabilities, principle of 388
Equation of motion 3
Equivalence class 28
Equivalence relation 27
Euclidean spaces 18
Euclidean spacescomplete orthonormal system in see Euclidean spaces orthonormal
Euclidean spacesisomorphism of 23
Euclidean spacesorthogonal basis in 36
Euclidean spacestensor products of 137
Euclidean spacesunitary equivalent see Euclidean spaces isomorphism
expectation value 263 277 see
Extension Principle 188
Fadeev, L.D. 594 595
Fatou's lemma 287
Fermi — Dirac statistics 307
fermions 353
Field 58 see Boolean
Fomin, S.V. 171 597
Fourier coefficient 38
Fragments 574
Fragments, internal energy of 579
Fredhold determinant, modified 492
Fredhold determinant, modified, first minor of 492
Fredholm theory 491
Free states 395 396
Friedrichs, K. 595
Fubini's theorem 96
Function, appropriate symmetrization of 312
Function, Hoelder continuous 561
Function, Riemann integrable 90
Function, spectral 235
Function, square integrable 101
Function, total variation of 444
Functional see also Vector spaces
Functional, bounded 182
Functional, continuous 182
Functional, linear 182
Garding, L. 342 596
Gelfand triples see Hilbert spaces rigged
Gibson, A.G. 593 596
Glazman, I.M. 256 309 595
Gottfried, K. 171 596
Green function 470
Green function, advanced 471
Green function, free advanced 489
Green function, free retarded 489
Green function, full 492 493
Green function, full, series expansion of 494
Green function, retarded 471
Green function, symmetry properties of 498
Green, T.A. 550 594 596
Ground state 168
Hack, M.N. 594 596
Hahn's theorem 237
Halmos, P.R. 81 171 287 596
Hamiltonian 286
Hamiltonian of arrangement channel 579
Hamiltonian, eigenfunction expansion for 469
Hamiltonian, internal free 419
harmonic oscillator 5 5
Hefner, H. 262 598
Heisenberg's equation 3 294
Heisenberg's picture 293
Heisenberg's uncertainty principle 8
Heisenberg, W. 1 6 296 596
Hellinger and Toeplitz theorem 195
| Hilbert spaces 30 32 33 41 109 220
Hilbert spaces, Hilbert tensor products of 144 145
Hilbert spaces, isometric transformation of 212
Hilbert spaces, rigged 186
Hilbert, D. 595
Howland, J.S. 594 596
Hunziker, W. 594 596
Ikebe, T. 514 536 549 569 594 596
Ince, E.L. 596
Incident flux 403
Indicial equation 165
Inner product 18
Integral, Booliner 457
Integral, Lebesgue 90 114
Integral, Riemann — Stieltjes 440
Integral, Riemann — Stieltjes cross-iterated 441
Integral, Riemann — Stieltjes, improper 441
Interacting state 397
Interaction picture 298
Intertwining property see Wave opration
Isometric operators and transfortmations 212
Isomorphism of Euclidean spaces 23
Jauch, J.M. 390 428 593 594 596
Jordan, T.F. 439 593 594 596
Kato, T. 256 365 367 390 506 530 594 596
Kernel,  see Hilbert — Schmidt kernel
Kernel, Hilbert — Schmidt 491 492
Kernel, time class 491
Kodaira, K. 594 597
Kolmogorov, A.N. 171 597
Krein, M.G. 594 595
Krzywicki, A. 56 595
Kummer's series 165
Kuroda, S.T. 594 596 597
Laguerre functions 170
Landau, L.D. 594 597
Lanford, O.E. III 550 594 596
Lax, P.D. 597
Lebcsguc bounded convergence theorem 287
Lebesgue integral see Integral
Lebesgue monotone convergence theorem 92
Legendre functions, associated 152
Legendre polynomials, associated 167
Lifshitz, E.M. 56 171 597
Limic, N. 594 597
Limit point 503 see
Limit point, Weyl's criterion for 503
Limit, weak, strong, uniform see Operators sequences
Linear manifold see Vector spaces
Linear operator see Operators
Linear space see Vector spaces
Linear subspace see Vector subspace
Lippmann — Schwinger equations, perturbation solution of 456
Lippmann — Schwinger equations, Type I 447 529
Lippmann — Schwinger equations, Type I, integral version of 482
Lippmann — Schwinger equations, Type II 449 483
Low equation 481
Luguerre polynomials 170
Luguerre polynomials, generating functions of 171
MacLane, S. 56 595
Mapping, Borel measurable 115
Mapping, isometric 27
Mapping, isomorphism 175
Margenau, H. 262 390 597
Massey, H.S.W. 533 597
Matrix mechanics 297
Mean value theorem 461
Measurable space 67
Measurable space, simple 81
Measure 58 67
Measure spaces 76
Measure spaces, Cartesian product of 77
Measure, complex 232
Measure, continuous 240
Measure, extension of 70
Measure, finite 67 79 232
Measure, inner 79
Measure, Lebesgue 67 78 79 114
Measure, Lebesgue — Stieltjes 79
Measure, lower variation of 239
Measure, outer 71
Measure, probability 68
Measure, signed 236 237
Measure, spectral 231 407
Measure, upper variation 239
Measurement, determinative 6 401
Measurement, determinative, Born's correspondence rule for 262
Measurement, preparatory 6 264 266
Measurement, theory of 4 262 264
Messiah, A. 1 56 170 171 330 597
Metric 25
Metric space 25
Metric space, complete 26
Metric space, densely embedded 27
Misra, B. 390 593 596
Munroe, M.E. 90 171 597
Naimark, M.A. 56 597
Neighborhood 27
Nelson, E. 268 597
Nering, E.D. 56 597
Newton, R.G. 481 594 597
Norm 20
Norm, completeness in 30
Norm, convergence in 30
Norm, Hilbert — Schmidt 378
Norm, trace norm 379
Observables 2
Observables, compatible 260 262
Observables, complete set of 316 384
Observables, fundamental 270
Operators, adjoint 188
Operators, antilinear 173 see antilinear
Operators, bound of 178
Operators, bounded 242
Operators, bounded from above 501
Operators, bounded from below 501
Operators, canonically conjugate 329
Operators, closed 191
Operators, complete set of 315
Operators, completely continuous 368
Operators, density see Statistical operator
Operators, essentially self-adjoint 358
Operators, function of 272
Operators, graph of 191
Operators, Hermitian 127
Operators, Hilbert — Schmidt 376 491
Operators, hypermaximal see Self-adjoint operators
Operators, linear 173 186 192 see linear
Operators, linear, closure of 355
Operators, matrix representation of 175 176
Operators, monotone sequences of 242
Operators, projection see Projector
Operators, self-adjoint see Self-adjoint operators
Operators, sequences, strong limit of 230 231
Operators, sequences, uniform limit of 230
Operators, sequences, weak limit of 230 231
Operators, symmetric 192
Optical theorem 480
Optical theorem, generalized 479
Pap, A. 47 597
Park, J.L. 262 597
Parseval's relation 38
Partially isometric operators 417
Pauli's exclusion principle 168 307
Phase shifts 468 569
Phase space 2
Phillips, R.S. 597
Physical interpretation see Measurement theory
Planck constant 46
Plane waves, advanced distorted 466
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