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| Prugovecki E. — Quantum Mechanics in Hilbert Space |
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| Предметный указатель |
 operators 511
Accumulation point 27
Additive class see “Algebra Boolean”
Algebra, associative 174
Algebra, boolean 58 60
Algebra, commutative 175
Algebra, generated by observables 276
Algebra, maximally Abelian 328
Almost everywhere 90
Asymptotic completeness 552
Asymptotic condition, physical 455
Asymptotic condition, strong 418
Asymptotic Hilbert space 612
Asymptotic states in classical mechanics 417
Asymptotic states in interaction picture 474
Asymptotic states in multichannel scattering 600
Asymptotic states, incoming 418 455
Asymptotic states, modified 514
Asymptotic states, Moller 418
Asymptotic states, outgoing 418 455
Asymptotic states, physical 457
Asymptotic states, strong 418
Axioms 2
Axioms for spin and statistics 309
Banach space 30
Bauer’s formula 592
Bessel’s inequality 38
Bilinear form 137
Borel set 62
Born approximations 556
Born series 557 621
Born’s correspondence rule 262 266
Bose — Einstein statistics 307
Bosons 353
Bound state 49
Bound state, energy eigenvalues of 49
Bounded variation 465
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 “Operators” “Spectral
Channel, arrangement 596
Channel, concept of 596 597
Channel, energy 597
Channel, incoming 596
Channel, outgoing 596
Characteristic function 81
Characteristic subspace 227
Characteristic value see “Eigenvalue”
Characteristic vector see “Eigenvector”
Closed graph theorem 210
Closure 27
Cluster of particles 596
Cluster point see “Accumulation point”
Collision, rearrangement 598
Completion 27
Confidence function 410
Configuration representation 352
Confluent hypergeometric equation 165
Confluent hypergeometric function 165
Copenhagen school see “Measurement”
Correspondence rule 3 259
Coulomb interaction 164
Cross section, differential 426 436 510
Cross section, total 426 513
Cyclic vector 365
Decomposition of identity see “Spectral function”
Deficiency index 223
Deficiency subspace 223
Dense embedding 31
Dense set 27
Density matrix 402
Density operator 391
Diffraction effect 7
Dirac delta function 509
Direct sum of Euclidean spaces 133
Distance function see “Metric”
Dynamical law 2
Eigenfunction 491 498
Eigenfunction expansion 499
Eigennumber 491
Eigenvalue 48 226
Eigenvalue equation 47
Eigenvalue, degenerate 49
Eigenvalue, multiplicity of 534
Eigenvalue, nondegenerate 49
Eigenvector 226
Energy shell 510 620
Ensemble, state of 393
Equal a priori probabilities, principle of 394
Equation of motion 3
Equivalence, class 28
Equivalence, physical 293
Equivalence, relation 27
Euclidean spaces 18
Euclidean spaces, complete orthonormal system in see “Euclidean spaces orthonormal
Euclidean spaces, isomorphism of 23
Euclidean spaces, orthogonal basis in 36
Euclidean spaces, tensor products of 137
Euclidean spaces, unitary equivalent see “Euclidean spaces isomorphism
Evanescence 301
expectation value 263 277
Extension Principle 188
Faddeev equations 624 625
Fatou’s Lemma 287
Fermi — Dirac statistics 307
fermions 353
Field 58 (see also “Alegebra Boolean”)
Fourier coefficient 38
Fragments 596
Fragments, internal energy of 597
Fredholm determinant, modified 527
Fredholm determinant, modified, first minor of 527
Fredholm theory 526
Free states 418
Fubini’s Theorem 96
Function, appropriate symmetrization of 312
Function, Riemann integrable 90
Function, spectral 235
Function, square integrable 101
Function, total variation of 467
Functional see also “Vector spaces”
Functional, bounded 182
Functional, continuous 182
Functional, linear 182
Gelfand triples see “Hilbert spaces rigged”
Green’s function 501
Green’s function, advanced 503
Green’s function, free advanced 524
Green’s function, free retarded 524
Green’s function, full 502 528
Green’s function, full, series expansion of 529
Green’s function, partial wave 525
Green’s function, retarded 503
Green’s function, symmetry properties of 531
Green’s operator 501
Ground state 168
Hack’s theorem 610
Hahn’s theorem 237
Hamiltonian 286
Hamiltonian of arrangement channel 599
Hamiltonian, eigenfunction expansion for 500
Hamiltonian, internal free 442
Hamiltonian, time-dependent 292 372
harmonic oscillator 55
Heisenberg’s equation 3 294
Heisenberg’s picture 293
Heisenberg’s uncertainty principle 8
Hellinger and Toeplitz theorem 195
| Hilbert spaces 30 32 33 41 109 220
Hilbert spaces, equipped 498
Hilbert spaces, extended 186
Hilbert spaces, Hilbert tensor products of 144 145
Hilbert spaces, isometric transformation of 212
Hilbert spaces, rigged 186
Idempotent 200
Identification operator 613
Incident flux 426
Indicial equation 165
Inertial frame 4
Inner product 18
Integral, Bochner 480
Integral, Lebesgue 90 114
Integral, Riemann — Stieltjes 463
Integral, Riemann — Stieltjes, cross-iterated 464
Integral, Riemann — Stieltjes, improper 464
Integral, spectral 483
Integral, time-ordered 372
Interacting state 420
Interaction picture 298
Intertwining property see “Wave operators”
Isometric operators and transformations 212
Isomorphism of Euclidean spaces 23
Kato’s theorem 367
Kernel,  see “Kernel Hilbert — Schmidt”
Kernel, Hilbert — Schmidt 526
Kernel, trace class 526
Kummer’s series 165
Laboratory frame of reference 119
Laguerre functions 170
Laguerre polynomials 170
Laguerre polynomials, generating function of 171
Lebesgue bounded (dominated) convergence theorem 287
Lebesgue intergral see “Integral”
Lebesgue monotone convergence theorem 92
Legendre functions, associated 152
Legendre polynomials, associated 167
Limit point 537 (see also “Accumulation point”)
Limit point, Weyl’s criterion for 537
Limit, strong see “Operators sequences”
Limit, uniform see “Operators sequences”
Limit, weak see “Operators sequences”
Linear manifold see “Vector spaces”
Linear operator see “Operators”
Linear space see “Vector spaces”
Linear subspace see “Vector subspace”
Liouville equation 397
Liouville space 405
Lippmann —Schwinger equations for  511
Lippmann —Schwinger equations for eigenfunctions 503 618
Lippmann —Schwinger equations in Hilbert space 470
Lippmann —Schwinger equations, perturbation solution of 456
Lippmann —Schwinger equations, solution-type 472
Lippmann —Schwinger equations, two-Hilbert space 615
Mapping, Borel measurable 115
Mapping, isometric 27
Mapping, isomorphism 175
Matrix mechanics 297
Mean value theorem 490
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, positive operator-valued 406
Measure, probability 68
Measure, signed 236 237
Measure, spectral 231
Measure, upper variation 239
Measurement, determinative 6 262 424
Measurement, determinative, Born’s correspondence rule for 262
Measurement, preparatory 6 264 266
Measurement, theory of 4 262 264
Metric 25
Metric space 25
Metric space, complete 26
Metric space, completion 27
Metric space, densely embedded 27
Moller wave operators 421 603
Momentum representation 354
Monotone class of sets 63
Monotonic sequence of operators 242
Neighborhood 27
Norm 20
Norm, completeness in 30
Norm, convergence in 30
Norm, Hilbert — Schmidt 384
Norm, Rollnik 545
Norm, trace norm 386
Observables 2
Observables, compatible 260 262
Observables, complete set of 316 498
Observables, expectation value 277
Observables, fundamental 270
Operators, adjoint 188
Operators, antilinear 173 (see also “Transformations antilinear”)
Operators, asymptotically compensating 515
Operators, bound of 178
Operators, bounded 242
Operators, bounded, from above 535
Operators, bounded, from below 535
Operators, bounded, relative to 360
Operators, canonical form 379
Operators, canonically conjugate 329
Operators, closed 191
Operators, compact 375
Operators, complete set of 315
Operators, completely continuous 375
Operators, core 366
Operators, density see “Statistical operator”
Operators, essentially self-adjoint 358
Operators, extension 186
Operators, finite-rank 377
Operators, function of 272
Operators, graph of 191
Operators, Hermitian 127
Operators, Hilbert — Schmidt 383
Operators, hypermaximal see “Self-adjoint operators”
Operators, linear 173 186 192 linear”)
Operators, linear, closure of 355
Operators, matrix representation of 175 176
Operators, monotone sequences of 242
Operators, positive definite 381
Operators, projection see “Projector”
Operators, relative bound 361
Operators, restriction 186
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 513
Optical theorem, generalized 513
Orthogonal system 21
Orthonormal basis 36
Parseval’s relation 38
Partially isometric operators 440
Pauli’s exclusion principle 168 307
Phase shifts 497 589 593
Phase space 2
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