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| Àâòîðèçàöèÿ |
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| Ïîèñê ïî óêàçàòåëÿì |
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| Amrein W.O., Sinha K.B., Jauch J.M. — Scattering Theory in Quantum Mechanics: Physical Principles and Mathematical Methods |
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| Ïðåäìåòíûé óêàçàòåëü |
 -algebra 547
(A1) - (A3) 140—141
(B1) - (B3) 580 585 593 614—618
(Strongly) singular potentials 167—168 341—342 347 387 492
A-bound(ed) 315—321 325
A-compact 318—321
Abelian algebra 548 562
Absolutely continuous operator 209 226—227 236 392
Absolutely continuous part 209
Absolutely continuous spectrum 209
Absolutely continuous vector 208 210
Absorption of states 167 305
Addition theorem for spherical harmonics 495
Adjoint 44—47 63
Affiliated 559
Angular momentum operators 457—459 498—501
Angular momentum, total 459 500—501
Anti-unitary operator 150
Asymptotic completeness 141 355—357 362—363 365 368 375—387 392 447 474 480 502 543 561 579 635—636 667—668
Asymptotic completeness, strong 357 426—434 438
Asymptotic condition 16—17 133—148 153—158 545—554 556—557 576—581 587 593
Asymptotic condition, evolution group 584
Asymptotic condition, Hamiltonian 584
Asymptotic condition, Hilbert space 575 584—586 595
Beam 5—6 13 282
Bessel function 496—498
Bessel inequality 25
Binding energy 592—594
Born approximation 253 509—516
Born approximation, - , partial wave 523
Born series 253 505—515 525
Bound state 262—269 572 589 607—609
Boundary values of holomorphic function 335 349—353 389—390
Bounded below, operator 319
Bounded below, spectral family 181
Bounded linear functional 29 434
Bounded operator 40—42 46
Branching ratio 12—13 628
Breit ? Wigner formula 494
C*-algebra 547 556 560
Cauchy sequence 23 60
Cayley transform 233
Center-of-mass coordinate 301 605
Chain rule 172
Channel 10 589—591
Channel, evolution group 592 625
Channel, Hamiltonian 591—592 623—625
Channel, Hamiltonian, spectral representation of 623—625 659—660
Channel, scattering operators 593—594 598 625—626 663
Channel, subspace 590—591 659
Channel, wave operators 592 598 614—618
Characteristic function 32
Closable operator 38 45
Closed operator 38—39 97
Closure of a manifold 28
Closure of an operator 38 40 45 88—89
Cluster 571
Cluster property of wave operators 637—639
Cluster, evolution group 572—573 615
Cluster, Hamiltonian 570—571 574 610—613
Cluster, observable 587
Cluster, scattering operator 581—584 596—597
Cluster, scattering operator, for three-body system 663—667
Cluster, subspace 570 573—575 590 610—611
Cluster, wave operators 580—582 585—586 595—596 614—618 643
Commutant 547
Commutativity 43 112 186—188 222
Compact operator 66—75 629 676
Compact operator, canonical expansion of 73
Completeness of H 20—21 31
Conservation of energy 146 583
Constant of motion 112 154—157 547
Continuity in Hilbert — Schmidt norm 79
Continuity of vector- and operator- valued functions 160 79
Continuous part of A 205
Continuous spectrum 204—207
Convergence in norm 60 62
Convergence in the mean 42 87
Cook — Hack criterion 327 346
Coulomb potential 269 323 328 528—531 539 542 561
Coupling constant 362
Cross section 12 14 282—288 623—628
Cross section, (averaged) total 14 291—297 309 339 353 466—468 510—513 520 627—628 663—667
Cross section, differential 13—15 286—289 302—303 339 468 474—475 515—516 519 525 627 639
Cyclic vector 548—549
Decay 11—12 168
Decomposable operator 219—224 643
Delta function potential 345
Dense set 20 27 28
Density operator 102 157
Detailed balance 292
Deuteron 10 570
Diagonalizable operator 177 219—222
Differential operator 54 106—108 475—480
Diffraction 5
DIMENSION 26
Direct integral 227
Direct sum 80—82 98 469
Discrete spectrum 211 324
Distorted wave Born approximation 525—526
Domain 37
Dressing transformation 542
Dual 434
Efimov effect 668
Eigenfunction expansion 396 411—415 434—439
Eigenfunctions 396—398 406—420 425 437—439 450 514 517—518 525 668
Eigenfunctions, partial wave 482—492
Eigenvalue 68—69 186
Eigenvalue problem 176
Eigenvalue, embedded in continuum 206 427—428 449—450 502 634 642
Eigenvector 68—69 111—112 186
Eikonal approximation 512
Eisenbud — Wigner relation 277 307
Elastic scattering 8 146 593 627—628
Elementary system 2 567
Endoergic reaction 9
Energy Observable 112 146 553
Energy renormalization 155 554
Equality of operators 37
Equivalence class 31 83 217
Equivalent functions 31 217
Essential spectrum 211—213 319 324 611—613 629—634
Essential supremum 57
Essentially bounded 57
Essentially self-adjoint 55 57 326 353 501
Evaluation functional 406—420 435—439
Exceptional point 428—434 490 502 508
Exceptional set 364 432—433 655—658
Exceptional vector 428—434 503
Exoergic reaction 9
expansion 26
expectation value 103 152 156
Extension 37
Factorization of potential 296 357 372
Faddeev equations 667
Feebly oscillating 532 553 563
Final set 51
Final state 138 153
Finer partition 637
Finite rank operator 65 98
Flux 308—309 420
Form domain 343
Form-bounded 344
Forward direction 281 625 628
Forward scattering amplitude 291—292 628
Fourier transform(ation) 33—36 42—43 86—87 455
Fourier transform(ation), generalized 408—415 436—438
Fredholm alternative 67—68
Free evolution 118—125 129 134 464
Free Hamiltonian 115 117—118 134 224—225 461—463 475—480 602 606
| Free Hamiltonian, absolute continuity of 209 225 602
Free Hamiltonian, spectral representation of 224—225 662—663
Free propagator 120—122
Friedrichs extension 344
Function of an operator 198—201 242
Function space 30—31 49 57 128
Functional calculus 198—201 242
Fundamental set 61
Gelfand triplet 435
Generalized wave operators see "Wave operators"
Graph 88—89
Green's function 237
Green's function, advanced and retarded free 370
Green's function, advanced and retarded total 440
Green's function, free 370 390—391
Green's function, partial wave 481
Green's function, total 439—440
Half-width 494
Hamiltonian 111 see
Hard core 348
harmonic oscillator 325 354
Heisenberg equation of motion 113
Heisenberg picture 113
High energy behaviour 297 309 505—516 522—526
Hilbert space 19—21
Hilbert — Schmidt kernel 76—77 290—291
Hilbert — Schmidt norm 74 77 98
Hilbert — Schmidt operator 74—79 290—291
Holomorphic 202
Hoólder continuity 256
Hoólder inequality 128
Hunziker's theorem 611—613 629—634
Identical particles 8 298 571
Identity operator 43
Inelastic scattering 8—9 581 594 627—628
Infinitesimal generator 101
Initial set 51
Initial state 137 156 278—287
Injection operator 575
Integral operator 76 290—291
Integral, Riemann — Stieltjes 183 240
Integral, Riemann, of operator-valued function 163—165
Integral, Riemann, of vector-valued function 159—163
Integral, spectral 239—244 256—257
Interaction 2 134 574 602—603 607
Interference 5
Intertwining relation 143 155 214 553—554 582—583 625—626
Invariance principle 171
Invariant scattering system 149 456—457 586—587
Inverse Fourier transformation 34—36 42—43
Inverse operator 44
Inverse scattering problem 15
Invertible operator 44
Isolated eigenvalue 68
Isometry 50
Isomorphism 98
Jost function 486—493 502—503
Kernel, of integral operator 76
Laboratory system 303
Laplacian 115
Laplacian in spherical coordinates 475
Lebesgue dominated convergence theorem 87
Legendre polynomial 495—496
Levinson's theorem 494
Limit in the mean 42 87
Linear manifold 27
Linear mapping 37
Linear operator 37
Lippmann — Schwinger equations 238 246 252 256 411—414 439 596 598
Lippmann — Schwinger equations, long range 544
Lippmann — Schwinger equations, partial wave 482
Long range potentials 148 328 528—545 636—637
Low energy behaviour 516—522
Lower bound of a spectral family 180
Lower bound of an operator 319
Magnetic vector potential 342
Manifold, linear 27
Maximal abelian algebra 556
Maximal differential operator 476—480
Measurable family of operators 219
Measurable family of vectors 216
Miller operators 165
Minimal differential operator 476—480
Mixed state 103
Modified free evolution 155—156 529—537 540—542 550—553 556—559
Momentum algebra 555—556 561 563
Momentum operator 106—108 602
Multichannel scattering 10 142 566—676
Multiplication operator, maximal 57—59
Multiplicity 69 177 227
Neumann functions 496
Neumann series 63
Norm continuity 79
Norm of a vector 20—22
Norm of an operator 40 43 46 58 98 229
Normal operator 199 231
Null space 190 236
Observable 103
Observable and scattering 152—158 545—552 557—561
On-shell part 253—254
On-shell S-operator see "S-matrix" "R-matrix"
Operator 37
Operator, algebra 546—547 550
Operator, between two Hilbert spaces 400
Optical theorem 291 512 628
Orthogonal 24
Orthogonal complement 28
Orthonormal basis 25—26
Orthonormal sequence 25
Pair potential 302 574 602
Parseval relation 26
Part of an operator 187
Partial isometry 49—51
Partial wave analysis 460—468 480—494 520—525
Partial wave subspace 460
Particle 2 105—109 116
Partition 159 571
Phase shift 464—467 489—494 520—525
Plane wave 396 498
Point of constancy (increase) 180
Point spectrum 204
Polar decomposition 97—98 190 235 557
Polarization identity 97
Polarized beam 9 474—475
Position operator 37 105—106 602
Position, probability measure 106—107 122—125
Positive operator 102
Potential 114 134
Potential scattering 134 302 327—328 332—333 366—375
Potential scattering, multichannel 601 614—618 635—639 663—668
Probability measure 104—105
Product of operators 43 46 62—63
Projection (orthogonal) 47—49 98
Projection theorem 28
Projection-valued measure 182
Projective representation 151 454
Pure point spectrum 204
Pure state 103
Purely continuous spectrum 204
Quadratic form (associated with an operator, closed, semi-bounded, symmetric) 343—346
Quasi-bound state 433 492—494 503 668
R-matrix see also "S-matrix" 253—255 283 336—339 420—424 447—448 465—467 474 489—492 505 509—513 520—526 625—626 663—667
RANGE 37
Rearrangement scattering 9 581 594 627—628
Reduced mass 299 603 624
Reduction of an operator 187
Regular solution 485—493 502—503
Relative coordinates 301 605—606 642
Relative momentum 299 588 605—606 642
Relatively bounded 315
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