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Amrein W.O., Sinha K.B., Jauch J.M. Ч Scattering Theory in Quantum Mechanics: Physical Principles and Mathematical Methods
Amrein W.O., Sinha K.B., Jauch J.M. Ч Scattering Theory in Quantum Mechanics: Physical Principles and Mathematical Methods

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Ќазвание: Scattering Theory in Quantum Mechanics: Physical Principles and Mathematical Methods

јвторы: Amrein W.O., Sinha K.B., Jauch J.M.

јннотаци€:

Everyone concerned with the teaching of physics at the advanced undergraduate or graduate level is aware of the continuing need for a modernization and reorganization of the basic course material. Despite the existence today of many good textbooks in these areas, there is always an appreciable tijne-lag in the incorporation of new viewpoints and techniques which result from the most recent developments in physics research. Typically these changes in concepts and material take place first in the personal lecture notes of some of those who teach graduate courses. Eventually, printed notes may appear, and some fraction of such notes evolve into textbooks or monographs. But much of this fresh material remains available only to a very limited audience, to the detriment of all. Our series aims to fill this gap in the literature of physics by presenting occasional volumes with a contemporary approach to the classical topics of physics at the advanced undergraduate and graduate level. Clarity and soundness of treatment will, we hope, mark these volumes, as well as the freshness of the approach.


язык: en

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1977

 оличество страниц: 692

ƒобавлена в каталог: 12.01.2010

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$\ast$-algebra      547
(A1) - (A3)      140Ч141
(B1) - (B3)      580 585 593 614Ч618
(Strongly) singular potentials      167Ч168 341Ч342 347 387 492
A-bound(ed)      315Ч321 325
A-compact      318Ч321
Abelian algebra      548 562
Absolutely continuous operator      209 226Ч227 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      44Ч47 63
Affiliated      559
Angular momentum operators      457Ч459 498Ч501
Angular momentum, total      459 500Ч501
Anti-unitary operator      150
Asymptotic completeness      141 355Ч357 362Ч363 365 368 375Ч387 392 447 474 480 502 543 561 579 635Ч636 667Ч668
Asymptotic completeness, strong      357 426Ч434 438
Asymptotic condition      16Ч17 133Ч148 153Ч158 545Ч554 556Ч557 576Ч581 587 593
Asymptotic condition, evolution group      584
Asymptotic condition, Hamiltonian      584
Asymptotic condition, Hilbert space      575 584Ч586 595
Beam      5Ч6 13 282
Bessel function      496Ч498
Bessel inequality      25
Binding energy      592Ч594
Born approximation      253 509Ч516
Born approximation, - , partial wave      523
Born series      253 505Ч515 525
Bound state      262Ч269 572 589 607Ч609
Boundary values of holomorphic function      335 349Ч353 389Ч390
Bounded below, operator      319
Bounded below, spectral family      181
Bounded linear functional      29 434
Bounded operator      40Ч42 46
Branching ratio      12Ч13 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 589Ч591
Channel, evolution group      592 625
Channel, Hamiltonian      591Ч592 623Ч625
Channel, Hamiltonian, spectral representation of      623Ч625 659Ч660
Channel, scattering operators      593Ч594 598 625Ч626 663
Channel, subspace      590Ч591 659
Channel, wave operators      592 598 614Ч618
Characteristic function      32
Closable operator      38 45
Closed operator      38Ч39 97
Closure of a manifold      28
Closure of an operator      38 40 45 88Ч89
Cluster      571
Cluster property of wave operators      637Ч639
Cluster, evolution group      572Ч573 615
Cluster, Hamiltonian      570Ч571 574 610Ч613
Cluster, observable      587
Cluster, scattering operator      581Ч584 596Ч597
Cluster, scattering operator, for three-body system      663Ч667
Cluster, subspace      570 573Ч575 590 610Ч611
Cluster, wave operators      580Ч582 585Ч586 595Ч596 614Ч618 643
Commutant      547
Commutativity      43 112 186Ч188 222
Compact operator      66Ч75 629 676
Compact operator, canonical expansion of      73
Completeness of H      20Ч21 31
Conservation of energy      146 583
Constant of motion      112 154Ч157 547
Continuity in Hilbert Ч Schmidt norm      79
Continuity of vector- and operator- valued functions      160 79
Continuous part of A      205
Continuous spectrum      204Ч207
Convergence in norm      60 62
Convergence in the mean      42 87
Cook Ч Hack criterion      327 346
Coulomb potential      269 323 328 528Ч531 539 542 561
Coupling constant      362
Cross section      12 14 282Ч288 623Ч628
Cross section, (averaged) total      14 291Ч297 309 339 353 466Ч468 510Ч513 520 627Ч628 663Ч667
Cross section, differential      13Ч15 286Ч289 302Ч303 339 468 474Ч475 515Ч516 519 525 627 639
Cyclic vector      548Ч549
Decay      11Ч12 168
Decomposable operator      219Ч224 643
Delta function potential      345
Dense set      20 27 28
Density operator      102 157
Detailed balance      292
Deuteron      10 570
Diagonalizable operator      177 219Ч222
Differential operator      54 106Ч108 475Ч480
Diffraction      5
DIMENSION      26
Direct integral      227
Direct sum      80Ч82 98 469
Discrete spectrum      211 324
Distorted wave Born approximation      525Ч526
Domain      37
Dressing transformation      542
Dual      434
Efimov effect      668
Eigenfunction expansion      396 411Ч415 434Ч439
Eigenfunctions      396Ч398 406Ч420 425 437Ч439 450 514 517Ч518 525 668
Eigenfunctions, partial wave      482Ч492
Eigenvalue      68Ч69 186
Eigenvalue problem      176
Eigenvalue, embedded in continuum      206 427Ч428 449Ч450 502 634 642
Eigenvector      68Ч69 111Ч112 186
Eikonal approximation      512
Eisenbud Ч Wigner relation      277 307
Elastic scattering      8 146 593 627Ч628
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      211Ч213 319 324 611Ч613 629Ч634
Essential supremum      57
Essentially bounded      57
Essentially self-adjoint      55 57 326 353 501
Evaluation functional      406Ч420 435Ч439
Exceptional point      428Ч434 490 502 508
Exceptional set      364 432Ч433 655Ч658
Exceptional vector      428Ч434 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      308Ч309 420
Form domain      343
Form-bounded      344
Forward direction      281 625 628
Forward scattering amplitude      291Ч292 628
Fourier transform(ation)      33Ч36 42Ч43 86Ч87 455
Fourier transform(ation), generalized      408Ч415 436Ч438
Fredholm alternative      67Ч68
Free evolution      118Ч125 129 134 464
Free Hamiltonian      115 117Ч118 134 224Ч225 461Ч463 475Ч480 602 606
Free Hamiltonian, absolute continuity of      209 225 602
Free Hamiltonian, spectral representation of      224Ч225 662Ч663
Free propagator      120Ч122
Friedrichs extension      344
Function of an operator      198Ч201 242
Function space      30Ч31 49 57 128
Functional calculus      198Ч201 242
Fundamental set      61
Gelfand triplet      435
Generalized wave operators      see "Wave operators"
Graph      88Ч89
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 390Ч391
Green's function, partial wave      481
Green's function, total      439Ч440
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 505Ч516 522Ч526
Hilbert space      19Ч21
Hilbert Ч Schmidt kernel      76Ч77 290Ч291
Hilbert Ч Schmidt norm      74 77 98
Hilbert Ч Schmidt operator      74Ч79 290Ч291
Holomorphic      202
Hoуlder continuity      256
Hoуlder inequality      128
Hunziker's theorem      611Ч613 629Ч634
Identical particles      8 298 571
Identity operator      43
Inelastic scattering      8Ч9 581 594 627Ч628
Infinitesimal generator      101
Initial set      51
Initial state      137 156 278Ч287
Injection operator      575
Integral operator      76 290Ч291
Integral, Riemann Ч Stieltjes      183 240
Integral, Riemann, of operator-valued function      163Ч165
Integral, Riemann, of vector-valued function      159Ч163
Integral, spectral      239Ч244 256Ч257
Interaction      2 134 574 602Ч603 607
Interference      5
Intertwining relation      143 155 214 553Ч554 582Ч583 625Ч626
Invariance principle      171
Invariant scattering system      149 456Ч457 586Ч587
Inverse Fourier transformation      34Ч36 42Ч43
Inverse operator      44
Inverse scattering problem      15
Invertible operator      44
Isolated eigenvalue      68
Isometry      50
Isomorphism      98
Jost function      486Ч493 502Ч503
Kernel, of integral operator      76
Laboratory system      303
Laplacian      115
Laplacian in spherical coordinates      475
Lebesgue dominated convergence theorem      87
Legendre polynomial      495Ч496
Levinson's theorem      494
Limit in the mean      42 87
Linear manifold      27
Linear mapping      37
Linear operator      37
Lippmann Ч Schwinger equations      238 246 252 256 411Ч414 439 596 598
Lippmann Ч Schwinger equations, long range      544
Lippmann Ч Schwinger equations, partial wave      482
Long range potentials      148 328 528Ч545 636Ч637
Low energy behaviour      516Ч522
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      476Ч480
Measurable family of operators      219
Measurable family of vectors      216
Miller operators      165
Minimal differential operator      476Ч480
Mixed state      103
Modified free evolution      155Ч156 529Ч537 540Ч542 550Ч553 556Ч559
Momentum algebra      555Ч556 561 563
Momentum operator      106Ч108 602
Multichannel scattering      10 142 566Ч676
Multiplication operator, maximal      57Ч59
Multiplicity      69 177 227
Neumann functions      496
Neumann series      63
Norm continuity      79
Norm of a vector      20Ч22
Norm of an operator      40 43 46 58 98 229
Normal operator      199 231
Null space      190 236
Observable      103
Observable and scattering      152Ч158 545Ч552 557Ч561
On-shell part      253Ч254
On-shell S-operator      see "S-matrix" "R-matrix"
Operator      37
Operator, algebra      546Ч547 550
Operator, between two Hilbert spaces      400
Optical theorem      291 512 628
Orthogonal      24
Orthogonal complement      28
Orthonormal basis      25Ч26
Orthonormal sequence      25
Pair potential      302 574 602
Parseval relation      26
Part of an operator      187
Partial isometry      49Ч51
Partial wave analysis      460Ч468 480Ч494 520Ч525
Partial wave subspace      460
Particle      2 105Ч109 116
Partition      159 571
Phase shift      464Ч467 489Ч494 520Ч525
Plane wave      396 498
Point of constancy (increase)      180
Point spectrum      204
Polar decomposition      97Ч98 190 235 557
Polarization identity      97
Polarized beam      9 474Ч475
Position operator      37 105Ч106 602
Position, probability measure      106Ч107 122Ч125
Positive operator      102
Potential      114 134
Potential scattering      134 302 327Ч328 332Ч333 366Ч375
Potential scattering, multichannel      601 614Ч618 635Ч639 663Ч668
Probability measure      104Ч105
Product of operators      43 46 62Ч63
Projection (orthogonal)      47Ч49 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)      343Ч346
Quasi-bound state      433 492Ч494 503 668
R-matrix      see also "S-matrix" 253Ч255 283 336Ч339 420Ч424 447Ч448 465Ч467 474 489Ч492 505 509Ч513 520Ч526 625Ч626 663Ч667
RANGE      37
Rearrangement scattering      9 581 594 627Ч628
Reduced mass      299 603 624
Reduction of an operator      187
Regular solution      485Ч493 502Ч503
Relative coordinates      301 605Ч606 642
Relative momentum      299 588 605Ч606 642
Relatively bounded      315
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