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Reed M., Simon B. — Methods of Modern mathematical physics (vol. 3) Scattering theory
Reed M., Simon B. — Methods of Modern mathematical physics (vol. 3) Scattering theory

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Название: Methods of Modern mathematical physics (vol. 3) Scattering theory

Авторы: Reed M., Simon B.

Аннотация:

Scattering theory is the study of an interacting system on a scale of time and/or distance which is large compared to the scale of the interaction itself. As such, it is the most effective means, sometimes the only means, to study microscopic nature. To understand the importance of scattering theory, consider the variety of ways in which it arises. First, there are various phenomena in nature (like the blue of the sky) which are the result of scattering. In order to understand the phenomenon (and to identify it as the result of scattering) one must understand the underlying dynamics and its scattering theory. Second, one often wants to use the scattering of waves or particles whose dynamics on knows to determine the structure and position of small or inaccessible objects. For example, in x-ray crystallography (which led to the discovery of DNA), tomography, and the detection of underwater objects by sonar, the underlying dynamics is well understood. What one would like to construct are correspondences that link, via the dynamics, the position, shape, and internal structure of the object to the scattering data. Ideally, the correspondence should be an explicit formula which allows one to reconstruct, at least approximately, the object from the scattering data. The main test of any proposed particle dynamics is whether one can construct for the dynamics a scattering theory that predicts the observed experimental data. Scattering theory was not always so central the physics. Even thought the Coulomb cross section could have been computed by Newton, had he bothered to ask the right question, its calculation is generally attributed to Rutherford more than two hundred years later. Of course, Rutherford's calculation was in connection with the first experiment in nuclear physics.


Язык: en

Рубрика: Математика/Математическая Физика/Учебники/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1979

Количество страниц: 463

Добавлена в каталог: 24.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L^p$ inequalities      32
Abelian limits      105
Absolute value of an operator      196
Absolutely continuous subspace      230
Acoustical scattering      184—243
action      279
Adjoint, Banach space      185
Adjoint, Hilbert space      186
Adjoint, unbounded operator      252
Admissible function      29
Agmon potential      439
Agmon — Kato — Kuroda theorem      439
Analytic Fredholm theorem      201
Analytic function, vector-valued      189—190
Analytic S-matrix hypothesis      96
Antibound states      144
Approximate identity      251 9
Associated Legendre functions      151
Asymptotic completeness      4
Asymptotic completeness, weak      3
Asymptotic Hilbert space      85
Asymptotic left inverse      35
Asymptotically equivalent      35
Atomic coordinates      78
Avron — Herbst theorem      61
Axiomatic quantum field theory      62
B.L.T.theorem      9
Baire measure      105 110
Banach space      67
Beloporskii — Birman theorem      36
Bessel’s equation      153
Birman’s theorem      28
Bogoliubov transformation      316
Boldface convention      7
Boltzmann equation      244
Born amplitude      109
Born series      109
Bounded operator      8
Breakup processes      77
Broken invariance      282
Canonical ellipse      151
Canonical form for compact operators      203
Capture processes      76
Cauchy sequence      5
Central force      13
Central potentials      121—168
Central potentials, almost      175
Chain rule      18
Channel      84
Channel, eigenenergies      84
Channel, embedding      85
Channel, Hamiltonian      85
Channel, Hilbert space      85
Channel, wave operators      85
Charge operator      300
Charge, conformal      275
Charged free scalar Boson field      300
Closed graph theorem      83
Closed operator      250
Closed quadratic form      277
Cluster decomposition      79
Cluster Hamiltonian      79
Cluster properties, of TVEV      324
Cluster properties, spatial      75 93—96
Clustered channel wave operators      82
Clustered Jacobi coordinates      79
Commuting (unbounded) operators      271—272
Compact operators      199 (see also “Relatively compact” “Relatively
Compact operators, determinant      323 382
Compact operators, general theory      198—206 316—338
Compact operators, Hilbert — Schmidt      210
Compact operators, ideal theory      41—44
Compact operators, resolvent      244—260
Compact operators, trace class      206—213
Compact support, distributions      319 178
Compact support, functions      111
Complete wave operators      19 35 88
Complete wave operators, asymptotically      4 18
Complete wave operators, weakly asymptotically      3 18
Cone property      204
Conformal charge      275 285
Conformal transformation      285
Conserved current      281
Continuous functional calculus      222
Contraction      151 235
Convolution, distributions      7
Convolution, functions      6
Cook — Hack theorem      56
Cook’s method      20
Coordinates, atomic      78
Coordinates, clustered Jacobi      79
Coordinates, Jacobi      78
Core      256
Critical value      449
Cross-section measure      15
Cumulants      381
Currents, conserved      278—285
Decomposable operator      123
Decomposition, of a channel      93
Deficiency indices      138
Differential cross section      15
Dilation current      282
Dilation transformation      282
Direct sum of Banach spaces      78
Direct sum of Hilbert spaces      40
Dirichlet Green’s function      206
Dirichlet Laplacian      263
Discrete spectrum      236
Dispersion relations      116
Distributions, compact support      139 178
Distributions, tempered      134
Dollard — Friedman theorem      161
Domain, analytic function      189
Domain, form      276
Domain, function      2
Domain, unbounded operator      249
Dominated Convergence Theorem      17 24
Dual space      43 72
Dynamical cut      145
Dyson expansion      282
EBFM S-matrix      4
Eigenfunction expansions      96
Eigenfunction expansions, auxiliary space method      122
Eigenvalue      188
Eigenvector      188
Elastic scattering      76
Electric field scattering      59
Elliptic operator      449
Elliptic regularity      49
Embedding transformation      86
Energy representation      123
Energy shell      108
Energy-momentum tensor      282
Enss potential      332
Enss’s Theorem      333
Equivalent measures      215
Essential support of an operator      393
Essentially self-adjoint      256
Euler — Lagrange equation      278
Exceptional set      99
Excitation collisions      77
Extension of an operator      250
External field scattering      293—316
False poles      145
Fatou’s theorem      233
Fiber      123
Finite mean free path      250
First resolvent formula      191
Fock space      53
FORM      see also “Quadratic forms”
Form, core      277
Form, domain      276
Form, domain, of operator      277
Forward scattering amplitude      117
Fourier inversion theorem      3
Fourier transform      1
Free Green’s function      102 208
Free Hamiltonian      85
Free Hamiltonian, charged scalar field      299
Free Hamiltonian, nonrelativistic quantum mechanics      552
Friedrichs’ extension      177
Functional calculus      222 225 245 263 286—287
Functions of rapid decrease      133
Generalized wave operators      17
Generator, group      268
Generator, semigroup      237 246
Graph      83 250
Green’s functions      102 103 206
Green’s functions, Dirichlet      206
Green’s functions, Neumann      206
Green’s functions, trace class properties      203
H-smooth      412
Haag — Ruelle theory      317
Hack’s theorem      82
Hahn — Banach theorem      75—77
Hamilton — Jacobi equation      183
Hamiltonian      303
Hamiltonian, free      55 220
Hamiltonian, time dependent      109
Hausdorff — Young inequality      11
Heisenberg model      286
Heisenberg picture scattering operator      307
Hermitian operator      see “Symmetric operator”
Hilbert space      36
Hilbert — Schmidt operators      210
Hilbert — Schmidt theorem      203
Holder’s Inequality      68 34
Holder’s inequality, matrices      385
Holder’s inequality, operators      41
Hughes — Eckart terms      78
Huygens’ principle      221
HVZ theorem      121
Impact parameter      14
Incoming spectral representation      219
Incoming subspace      211
Incoming translation representation      212
Infinitesimal generator, group      268l
Infinitesimal generator, semigroup      237 246
Infrared problem      381
Intercluster potential      79
Internal symmetry      404
Interpolation theorems      32
Invariance principle      31
Inverse Fourier transform      1
Iorio-O’Carroll theorem      424
Jacobi coordinates      78
Jauch S-matrix      322
Jost equation      137
Jost function      140
Jost solutions      139
Jost solutions for oscillatory potentials      155
K-system      369
Kato — Birman theory      22
Kato — Rosenblum theorem      26
Kato’s smoothness theorem      422
Kinematical cut      145
Kohn variational principle      147
Kupsch — Sandhas theorem      21
Kuroda — Birman theorem      27
Laplacian, Dirichlet      263
Laplacian, Neumann      263
Laplacian, on $\mathbb{R}^n$      54
Lavine’s theorem      429
Lax — Phillips method      210—241
Least action      279
Left-hand cut      145
Legendre polynomials      149
Legendre’s equation      149
Lehmann ellipse      119
Levinson’s theorem      142
Lippman — Schwinger equation      98
Local smoothness      433
Long-range potentials      169—183
Lorentz inversion      283
Magnetic field scattering      66
Magnetic spin waves (magnons)      286
Mass gap      319
Measurable functions, sets      14—16 19—24 104—111
Measurable unbounded operator-valued function      283
Measurable, weakly and strongly      64 115—117
Measure      19—25 104—111
Meromorphic Fredholm theorem      107
Monotone Convergence Theorem      17 24
Monotone convergence theorem, for nets      106
Mutually subordinate operators      28
Neumann Green’s function      206
Neumann Laplacian      263
Neutron transport equation      245
Noether’s theorem      278 279
Norm      8
Norm resolvent sense, convergence in      284—291
Norm, operator      9
Number operators      299
On-shell T-matrix      108
One-parameter unitary group      265
Open channels      124
Operator, adjoint, Banach space      185
Operator, adjoint, Hilbert space      186
Operator, adjoint, unbounded      252
Operator, bounded      8
Operator, compact      199
Operator, compact resolvent      244
Operator, contraction      235
Operator, decomposable      281
Operator, dilation      183
Operator, elliptic      112 346
Operator, energy (Hamiltonian)      303
Operator, general theory      81—84 182—216
Operator, Hamiltonian      303
Operator, hermitian      see “Operator symmetric”
Operator, Hilbert — Schmidt      210
Operator, ideals      41—44
Operator, infinitesimally form small      168
Operator, infinitesimally small      162
Operator, locally smooth      433
Operator, momentum      304 63
Operator, non-self-adjoint      316—338
Operator, norm      9
Operator, normal      246
Operator, positive      195
Operator, positivity improving      201
Operator, positivity preserving      201
Operator, relatively bounded      162
Operator, relatively compact      113
Operator, relatively form bounded      168
Operator, relatively form compact      369
Operator, resolvent      188 253
Operator, Schrddinger      79
Operator, self-adjoint      187 255
Operator, smooth      411—437
Operator, symmetric      255
Operator, tensor product      299
Operator, topologies      182—185 283—295 41—44 268—273
Operator, trace class      207—210
Operator, unbounded, general theory      249—312
Optical scattering      197
Optical theorem      111
Outgoing spectral representation      219
Outgoing subspace      211
Outgoing translation representation      212
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