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| Rodberg L.S., Thaler R.M. — Introduction to the quantum theory of scattering |
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| Предметный указатель |
Abstract vector space see "Vector space"
Addition of angular momentum see "Angular momentum"
Adiabatic switching 218
Adjoint matrix 171
Adjoint operator 171
Adjoint space 165
Adjoint vector 165
Analiticity see "Radial Green's function"
Angular momentum, addition of 286—299
Angular momentum, barrier 28
Angular momentum, conservation of 261—263
Angular momentum, eigenfunctions of 285—287
Angular momentum, orbital 27
Angular momentum, orbital, eigenstates of 241 245
Angular momentum, projection operator see "Projection operators"
Angular momentum, raising and lowering operators see "Raising and lowering operators"
Angular momentum, representation 241
Antilinear operator 268
Antisymmetrization of state vector 206—208
Antiunitary operator 269
Asymmetry left-right 306 313—316
Attenuation 370—371
Beam monitor 9
Bessel functions, integral representation of 123
Born approximation 144—149 158 183 291 324
Born approximation to phase shift 147
Born approximation, distorted wave 147—149 324 327—341 379
Born approximation, validity of 145—146
Born expansion 143—149 158 177 178 237 353
Born expansion, convergence of 144 153
Boundary condition 105 201
Boundary condition for scattering 13
Boundary condition, incoming-wave see "Incoming wave"
Boundary condition, outgoing-wave see "Outgoing wave"
Boundary condition, periodic 108
Boundary condition, regularity at origin 29
Boundary condition, relation to experimental situation 3
Bra 165
BRA-KET Symbolism 164 ff.
Bragg scattering 12
Breakup reaction 187 ff. 336—339
Breit — Wigner formula 380—383 388
Bremsstrahlung 339—341
Causality condition 136—137
Center of mass 2
Center-of-mass coordinate 250
Center-of-mass motion 260—261 331
Center-of-mass system 260
Channel 380
Channel spin 297—299 308
Channel, entrance 380
Channel, exit 380
Charge exchange operator 243
Charge exchange scattering 243 ff.
Classical limit see "JWKB Approximation"
Classical scattering formula 63
classical turning points see "Turning points"
Clebsch — Gordan coefficients 287—288
Closure 85 109 115
Closure approximation 359
Coherent part 366 ff.
Coherent wave 364—366
Collimator 4
Collision cross section see "Cross section differential"
Commutator 254
Commuting observables 166
comparison function see "Free particle comparison function"
Competing processes 244
Complete set 166
Completeness 85 168 232 234 245
Complex conjugate operator 270
Complex potential see "Potential"
Compound elastic scattering 388
Compton scattering 347
Conjugate variable 254
Conservation laws 249 ff.
Conservative potential 2
Continuous spectrum 109
Continuous variables 166
Contour integration 104
Contour of integration 101 110
Coordinate representation 168 345
Coulomb force 51
Coulomb function 63—72
Coulomb function in parabolic coordinates 66
Coulomb function, radial 65
Coulomb interference 71
Coulomb phase 72
Coulomb potential see "Scattering"
Cross section 6 187 225—226 299—307
Cross section for general scattering problem 193
Cross section for identical particles 208—210
Cross section for rearrangement collisions 202
Cross section, differential 8 21 195 303—305 312—313
Cross section, experimental definition of 21
Cross section, total 8
Cross section, unpolarized 305 315
Current 91 124
Current density 6 8
Current, conservation of 9 10 22 25 33 293—295
Damping equation 238 240—244 247
Delta function 166
Delta function in angular momentum representation 242
Delta function, source 128
Density matrix 311—313
Density of states 195—196 202
Detailed balance theorem 276
Detection probability 20
Detector 4 194
Determinantal method 156
Differential cross section see "Cross section"
Diffraction 61 358
Dirac delta function see "Delta function"
Dirac notation see "BRA-KET Symbolism"
Dirac operator formalism see "Operator formalism"
Discrete spectrum 84 109
Distorted wave approximation see "Born approximation"
Distorted wave Born approximation see "Born approximation"
Distorting potential see "Potential"
Double scattering 306
Double scattering, contribution to T matrix 359—360
Effective field 353
Effective incident wave 353 355 363 367
Effective incident wave operator 376
Effective interaction 386
effective mass 372
Effective range 47
Effective range expansion see "Phase shift"
Effective range, generalized 156
Eigen-phase shift 246
Eigenfunction expansion 100 see
Eigenfunctions 84 ff.
Eigenfunctions, normalized 85
Eigenvalue equation 166
Eigenvector expansion 167—169
Elastic scattering 2 26 187 329—332 357 363—379 381
Electromagnetic interaction 339
Energy conservation 186 255
Energy shell 160 343 see "T
Entrance channel see "Channel"
Exchange scattering 187 ff. 332—336
Exchange term, in identical particle scattering 209
Excited states 377
Existence of scattering operator 231—233
Exit channel see "Channel"
Exponential operator 212
Final state form of state vector see "State vector"
Final state Hamiltonian see "Hamiltonian"
Final state interaction 337 340
Final state potential see "Potential"
| Flux conservation see "Current conservation
Form factor 347 357 369
Fourier expansion 138 140
Fourier transform 169 342 344 347
Fraunhofer scattering 135
Fredholm determinant 150 155
Fredholm method 149—157
Fredholm method, expression for phase shift 154—156
Fredholm method, three-dimensional 156—157
Free particle 14
Free particle Hamiltonian 188
Free particle, comparison function 73 78
Fresnel scattering 135
Gallilean invariance 255—261
Gallilean transformation operator 256
Gauge invariance 339
Generator of transformation see "Transformation"
Green's function 73 ff. 107—121
Green's function for motion in non-Hermitian potential 120—121
Green's function for particle with spin 289—290
Green's function for unbounded domain 110
Green's function, as inverse operator 116
Green's function, asymptotic behavior 118—121
Green's function, eigenfunction expansion 125
Green's function, free particle 121
Green's function, general form of 112—114
Green's function, initial state 366
Green's function, integral equation for 134
Green's function, many-particle 121—126
Green's function, many-particle, asymptotic behavior of 123
Green's function, many-particle, for motion in potential 115—117 124—126
Green's function, operator form of 174—177
Green's function, outgoing-wave 110—112 114 128 191
Green's function, relation to radial Green's function 114—115
Green's function, singularity of 108
Green's function, symmetry of 116
Green's function, symmetry property 110
Green's function, time-dependent 136—141 212
Green's theorem 139
Hamiltonian 1
Hamiltonian, final state 333 334 336 339
Hamiltonian, hermiticity of see "Hermiticity"
Hamiltonian, initial state 328 352 366
Hankel function 123
Hartree potential see "Potential"
Heisenberg equation of motion 215
Heisenberg picture 215 ff.
Heitler damping equation see "Damping equation"
Hermitian matrix 171
Hermiticity 93 173 201 238 294 326
Hermiticity of K Matrix see "K Matrix"
Hilbert space see "Vector space"
Hypergeometric function 64
Identical particles 205—210
Impact parameter 59
Impulse approximation 341—350 353 356
Impulse approximation, validity of 348—350
Incident beam 190
Index of refraction see "Refractive index"
Inelastic scattering 187 ff. 194 331—332 341 347 358 364 378
Ingoing-wave 119
Ingoing-wave function 119
Initial state Green's function see "Green's function"
Initial state Hamiltonian see "Hamiltonian"
Initial state potential see "Potential"
Integral equation(s) for scattering amplitude 157—162
Integral equation(s) for time-dependent wave function 138—141
Integral equation(s) for wave function 127—136
Integral equation(s) of scattering theory 127 ff.
Integral equation(s) with distorted wave 130—131
Integral equation(s), solution of 127 ff.
Integral equation(s), stationary state 141
Integral equation(s), time-dependent derivation of 136—141
Integral, principal value of see "Principal value"
Interaction picture 212 ff. 214
Interference between Coulomb and nuclear scattering see "Coulomb interference"
Invariance principles 249 ff.
Invariance properties 313
Inverse operator 165
JWKB approximation 55—63
JWKB Approximation for Coulomb potential 63
JWKB Approximation, classical limit 59—63
JWKB Approximation, connection formulas 57
K matrix 34 76 227—248
K Matrix, hermiticity of 238 240
K Matrix, off energy shell 239
Ket 165
Kinetic energy operator 173 332 334 352
Kronecker delta 166
Laplacian operator in spherical coordinates 26
Laue conditions 358
Legendre expansion 114 265 see
Logarithmic derivative 35 90 100
magnetic quantum number 273
Many-body problem 351
Many-body system, scattering by see "Scattering"
Many-particle Green's function see "Green's function"
Matrix 170
Matrix element 170 182
Matrix methods in scattering theory 307—316
Mean free path 373
Mittag — Leffler theorem 87—90
Mixed representation 365
Momentum, conservation of 249—255
Momentum, representation 168
Momentum, total 251 254 259
Multiple scattering 351—356
Newton's second law 63
Normalization condition 166
normalization constant 31—32
Normalization of vectors in vector space 164 ff.
Operator 165
Operator equation for transition operator 183
Operator form of scattering equations 171—183
Operator formalism 163 ff.
Operator, antilinear see "Antilinear"
Operator, antiunitary see "Antiunitary"
Operator, representation, of see "Representation"
Optical potential 363—379
Optical potential, approximate form 366—369
Optical potential, approximations for 377—379
Optical potential, exact form of 373—377
Optical potential, local approximation to 368
Optical potential, multiple scattering expansion for 377—378
Optical theorem 9 10 22 25 33 146 183—186 226 235—237 242 293—295
Orbital angular momentum see "Angular momentum"
Ordinary scattering 187 ff. 329—332 384
Ordinary scattering, S matrix for see "S Matrix"
Orthogonal set 85 166
Orthogonality 231 see orthogonality
Orthogonality relation 166
Orthonormality 92
Orthonormality relation 108
Outgoing wave boundary condition 19 124 128 189
Outgoing wave Green's function see "Green's function"
Parabolic coordinates 66
Parity, conservation of 185 263—266
Parity, intrinsic 263
Partial wave expansion 281—282 292 see
Partial width 383 388
Pauli principle see "Identical particles"
Pauli spin matrix 270 280
Periodic boundary conditions see "Boundary conditions"
Permutation operator 206
Perturbation theory, time dependent 216
Phase amplitude method 52—63
Phase shift 29 32 383
Phase shift for square well 35—36 58
Phase shift, Born approximation, to see "Born approximation"
Phase shift, calculation of 25—44
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