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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 |
Relatively compact 318
Rellich theorem 319
Rellich — Kato condition 315
Resolution of the identity 179
Resolvent 127 200—203
Resolvent equation, first 202
Resolvent equation, second 249
Resolvent of free Hamiltonian 266—268 370
Resolvent set 201
Resolvent, holomorphy of 202
Resonance scattering 12 493—494
Restriction 38
Riccati — Bessel, —Hankel and —Neumann functions 496—498 482
Riesz representation theorem 29 97
Riesz — Fischer theorem 31
Rollnik potential 345—346 385
Rotation group 453—459 470 481 501
S-matrix see also "R-matrix" 226 229 253—255 277 489 518
S-operator 138 145—152 156 226 247 250—254 463—467 562 581—584 586—587 596—598 625
Scalar product 20 30 95
Scattering amplitude 286—293 339 421—426 448 465—468 514—516 518—519 525—526 627—628
Scattering angle 4 468
Scattering at large distances 331—333 349
Scattering channel see "Channel"
Scattering cross section see "Cross section"
Scattering into cones 279—282 308 544—545 618—623 640—642
Scattering length 519
Scattering operator see "S-operator"
Scattering states 136 166—168 262—269 303—305 569—570 607—609 636
Schatten — von Neumann ideal 449
Schroedinger Equation, radial 341—342 483
Schroedinger equation, time-dependent 110—111 237
Schroedinger equation, time-independent 237 396—398 437
Schroedinger operator 322 475—480
Schroedinger picture 113
Schwarz inequality 21
Screened potential 333 349
Self-adjoint operator 53 56—58 69—71 236 319 469
Separable Hilbert space 20—21 31—32
Separable interaction 333—339 353 392 451 513
Separating vector 548—549
Short range potentials 148 328
Simple scattering system 141
Simple spectrum 228 376—378 461 480 543
Singular part (of an operator) 209
Singular spectrum 209
Singular values 72—73 77
Singularly continuous operator 209 211
Singularly continuous part 209
Singularly continuous spectrum 209
Smoothness 380—382 392—393
span 70
Spatial isomorphism 559
Spectral family 104—107 179—183 221
Spectral integral 239—244 256—257
Spectral measure 180—182 207 360 389
Spectral multiplicity 227
Spectral representation 215—229 436
Spectral theorem 71 194—197 231—235
Spectral transformation 225—228 404—409 434—436 461—463
Spectrum 201
Spherical harmonics 495 498—501
Spherical symmetry 452—468 475—494 543
Spherically symmetric function 455
Spin 9 108—109 115 129 154 470
Spin-flip, spin-non-flip amplitude 474
Spin-orbit interaction 469—475
Square root 189 230 234
Square well 323 328
Stark potential 325
State 102—103
| Stationary state 111—112
Stationary state, scattering theory 244—255 382—385 544 595—598
Stone's theorem 100—102 125—127 130
Strong continuity 79 100 160
Strong convergence 23—24 59—63 95—96
Strong derivative 101 161
subspace 27 47—48
Subspace of absolute continuity 208 210 213
Subspace of continuity, of discontinuity 205—207 265—269 303—305
Subspace of singularity 208
Sum of operators 43—44
Support of a spectral family 180
Symmetric operator 52—57 173
Symmetry (group) 100 109 148—152 586—587
TARGET 5 289
Tensor product 83—86 98 501 599 629
Three-body problem 644—676
Threshold 594 626
Time delay 270—277 306—308
Time-evolution 109—113
Time-reversal 151 166 292—293 353 501 554 587
Total cross section see "Cross section"
Total evolution 133 576
Total Hamiltonian 134 322 341—346 463 471—473 476—480 603—605 607—613
Total Hamiltonian, absence of singularly continuous spectrum 426—432 451 634
Total Hamiltonian, absolutely continuous part 215 365 368 375 404—415 612—613 635
Total Hamiltonian, boundedness below 324 603 607
Total Hamiltonian, discrete spectrum 427 434 634 668
Total Hamiltonian, embedded eigenvalues 427—428 449—450 487 502 508 634 642
Total Hamiltonian, essential spectrum 323 611—613 629—634
Total Hamiltonian, Green's function 439—440
Total Hamiltonian, resolvent of 359—364 439 647—658
Total mass 299 605
Total momentum 299 310 588 605
Trace 77—78 98
Trace, class 78—79 294
Trace, criterion 386—387
Trace, norm 77 98
Triangle inequality 22
Two-Hilbert space formulation 584—586 594
Unbounded operator 40
Uniform boundedness principle 61
Uniform convergence 60 62—63
Unilateral shift operator 51 79
Unit ray 103
Unit vector 48
Unitarity of S 147 151 166 292 583—586 599
Unitary group 100—102 200
Unitary group, continuity of 100 129
Unitary operator 52 232
Unperturbed evolution 133 570—574
Unperturbed Hamiltonian 134
Upper bound of spectral family 180
Vector 19
Vector, representation 454—455
Vector-valued function 159 216
Virtual eigenvector see "Quasi-bound state"
Volterra integral equation 486 502
von Neumann algebra 550 556 560
Wave homomorphism 545—552 559—561
Wave operators 138—151 164 215 245—247 553 580—582 585—586 592 595—598 614—618
Wave operators, existence of 326—328 335 346—349 353 379 473 502 562 614—616 643
Wave operators, generalized 154—157 169 529 537—540 544 550—553 559—561
Wave vector 396
Weak continuity 79
Weak convergence 23—24 60—61 63
Weak coupling 362 368 375 508—509 635
Weak solutions 437
Weinberg — van Winter equations 669
Weyl — von Neumann theorem 324
Yukawa potential 323 328 524—526
Zero vector 19—20
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