Greiner W. — Relativistic quantum mechanics. Wave equations :: Электронная библиотека попечительского совета мехмата МГУ

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Greiner W. — Relativistic quantum mechanics. Wave equations

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Название: Relativistic quantum mechanics. Wave equations

Автор: Greiner W.

Аннотация:

Relativistic Quantum Mechanics. Wave Equations concentrates mainly on the wave equations for spin-0 and spin-1/2 particles. Chapter 1 deals with the Klein-Gordon equation and its properties and applications. The chapters that follow introduce the Dirac equation, investigate its covariance properties and present various approaches to obtaining solutions. Numerous applications are discussed in detail, including the two-center Dirac equation, hole theory, CPT symmetry, Klein's paradox, and relativistic symmetry principles. Chapter 15 presents the relativistic wave equations for higher spin (Proca, Rarita-Schwinger, and Bargmann-Wigner). The extensive presentation of the mathematical tools and the 62 worked examples and problems make this a unique text for an advanced quantum mechanics course.This third edition has been slightly revised to bring the text up-to-date.

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Рубрика: Физика/Общие курсы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: third edition

Год издания: 2000

Количество страниц: 424

Добавлена в каталог: 09.09.2005

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Предметный указатель

$\delta$ function      85
$\gamma$ emission      249
$\gamma$ matrices      255
$\gamma$ matrices in the Weyl representation      356
$\gamma$ radiation      263
$\Phi$ product (generalized scalar product)      33
$\Phi$ representation      32ff 36 277ff
$\Phi$ scalar product      69
$\Phi$ unitary      33 68
$\pi$ -mesic deuterium atom      67
$\pi$ -N interaction      83
$\Psi$ representation      36
$\widehat{P}\widehat{C}\widehat{T}$ theorem      323
$\widehat{P}\widehat{C}\widehat{T}$ transformation      318ff
$\widehat{\Sigma}$ -matrices      266
$\widehat{\Sigma}$ -operator for multispinors      350
Abelian group      399
Adjoint spinor      148
Adjoint wave equation      166
Angular momentum representation of left-handed neutrinos      340
Angular momentum representation of the Weyl equation      344
Angular momentum, inner      411
Angular momentum, operator of      411
Angular momentum, Quantum number      28
Anomalous magnetic moment      251 254
Anticommutation relations      101 129ff
Anticommutation relations of the Dirac matrices      337
Antineutrino      29
Antiparticles      27 76 238
Auger capture      65
Auger emission      249
Backward scattering      88
Bargmann — Wigner equations      352ff
Bargmann, Valentine      388
Baryon number      28
Basset formula      80
Bessel equation      56
Bessel functions      80
Bessel functions, $\beta^{\pm}$ decay      333
Bessel functions, asymptotic behaviour of      219
Bessel functions, inverse      333
Bessel functions, modified      81 219
Bessel functions, ordinary      81
Bessel functions, spherial      82
Bessel functions, spherical      219
Bethe — Salpeter equation      250 251
Bilinear covariants      151
Binding energies      48
Binding energies in a combined atom      274
Binding energies of an electron in a hydrogen atom      232
Bispinor      137
Bohr formula      232
Bohr radius of electrons      251
Bohr radius of the muon      249
Born approximation      86
Born series      86
Bose statistics      323
Bound states      200 206
Bound states of an electron in a hydrogen atom      233
Bound states, charge conjugation of      310ff
boundary conditions      328
Branch Cuts      85
C parity      28
C parity of the $\eta$ meson      30
C parity of the $\pi$ meson      30
Canonical formalism      12 70
Canonical Lagrange formalism      111
Casimir operator      412
Casimir operator of the Poincare group      399
Cayley — Klein parameters      404
Cayley, Arthur      415
Centre-of-mass system of muonic atoms      250
Champbell — Hausdorf relation      401
Charge conjugation      26 299ff 319
Charge conjugation matrix      359
Charge density of the Klein — Gordon equation      8
Charge parity, negative      27
Charge parity, positive      27
Charge radius of the pion      254
Charge-conjugate state      301
Charge-conjugated solution of the Dirac equation, energy of the      310
Charge-conjugated solution of the Dirac equation, momentum of the      310
Charge-conjugated solution of the Dirac equation, polarization of the      310
Charge-conjugated state of the Klein — Gordon field      26
Charge-conjugation operator      29 342
Charge-conjugation parity      28
Charge-conjugation symmetry      311
Charge-current density of the Klein — Gordon equation      8
Charged vector mesons      382
Chemical binding      261
Chew — Low interaction      83
Chew — Low model      95
Chiral representation      356
Chirality      356
Chirality for zero-mass particles      358
Chirality operator      357 364
Chirality, operator      356
Clebsch — Gordan coefficients      268
Clebsch — Gordon coefficients      212
Clifford algebra      356 359 372 384
Closure relation for unit spinors      171ff
Coherence      88
Collapse of the vacuum      232
Commutation relations      4 362
Commutation relations of angular momentum      266
Commutation relations of Kemmer matrices      365
Commutation relations of mixed tensors      393ff
Commutator expansion      286
Compton wavelength      1
Compton wavelength of the electron      252
Compton wavelength of the pion      43 60
Confluent hypergeometric functions      47 230 237 244 247
Confluent hypergeometric series      63
Conformal group      400
Conformal transformations, proper (special)      400
Conjugate momentum density      17
Conservation law      42
Construction of the vacuum      311
Continuity equation      99 103
Continuity equation for neutrino currents      337
Continuity equation for the Klein — Gordon field      42
Continuity equation of the Klein — Gordon equation      6
Continuum waves      248
Continuum waves of negative energy      199
Contravariant      2
Coordinate inversion      397
Correlation diagram      274
Correlation diagram, relativistic      274
Coulom barrier      261
Coulomb energy, expectation value of the      226
Coulomb gauge      51
Coulomb phase      248
Coulomb potential      42 122 234 258
Coulomb potential, two-centre      269
Coupled radial differential equations      234 239
Coupled radial differential equations for a Dirac particle in a Coulomb field      239
Coupling, anomalous      382
Coupling, dipole      382
Coupling, quadrupole      382
Covariance      104
CP symmetry for the Dirac neutrino      342
Creation and annihilation operators for photons      294
Current densities      41
Current density      76 104 147
Current density, convection      185
Current density, spin      186
Current of a wave packet      184 190
Current operator, charge conjugated      321
Darwin term      290
Decay of the vacuum in supercritical fields      276 332

Delta electrons      262
Delta rays      262
Demand boundary conditions      9
Densities, pseudoscalar      154 339
Densities, pseudovector      154
Densities, scalar      153 339
Densities, tensor      154
Densities, vector      154
Dielectric medium      253
Differential equations for radial functions      340
Dilatation      400
Dipole approximation      295
Dirac algebra      132
Dirac eigenvalue equation      321
Dirac equation      55 293
Dirac equation for neutrinos      341
Dirac equation in four-dimensional notation      128
Dirac equation in polar coordinates      263
Dirac equation with electromagnetic potentials      121
Dirac equation, covariance of the      130ff
Dirac equation, Majorana representation of the      155
Dirac equation, single-particle interpretation      111
Dirac equation, stationary      271
Dirac Hamiltonian, eigenvalues of the free      111
Dirac Hamiltonian, free      112
Dirac matrices      102 337
Dirac matrices, hermiticity of the      103
Dirac matrix      151
Dirac plane waves into the representation      283
Dirac sea      112 200 291 311
Dirac solution for positive/negative-energy free states      157ff
Dirac vacuum      238
Dirac, Paul Adrien Maurice      126
Direct product      412
Dual tensor      361
Effective mass of a scalar bound electron      209
Ehrenfest' s theorems      70 112 121
Eigenvalue equation for multispinors      348
Eigenvalue spectrum      203
Eigenvalue spectrum, symmetric      206
EINSTEIN's summation convention      3
Elastic scattering      87
electromagnetic field      41
Electromagnetic field tensor      4
Electron polarized      174
Electron-hole pair      262
Electron-positron pair creation      292
Electron-positron pair creation at the potential barrier      332
Energy conservation      84
Energy continuum, lower      117
Energy continuum, upper      117
Energy eigenvalue, double meaning of      69
Energy eigenvalues      221 222 225
Energy eigenvalues of the Dirac equation      259
Energy flux of the Schroedinger equation      20
Energy gap      231
Energy gap between electrons and positrons      210
Energy of the vacuum      293
Energy-momentum relation      20 100
Energy-momentum relation, nonrelativistic      4
Energy-momentum relation, relativistic      4 24
Energy-momentum tensor      16 17 34
Energy-momentum tensor of the free Dirac equation      114
Energy-momentum tensor of the Klein — Gordon field      12
Energy-momentum tensor of the Schroedinger equation      18
Energy-spin projectors      181ff
Ericson — Ericson, correction      92
Ericson — Ericson, potential      65
Euler — Lagrange equations      14 378 381
Euler — Lagrange equations for fields      16
Euler — Lagrange equations for the Klein — Gordon field      14
Exchange of massless photons      234
Exchange of massless scalar mesons      234
expectation value      35
Exponential potential      59
Extension of the leptons      254
Extension of the muon      254
External field approximation for muonic atoms      250
Fermi charge distribution      55
Fermi distribution      54 252
Fermi statistics      323
Fermi's golden rule      295
Fermions, left-handed      339
Fermions, right-handed      339
Feshbach — Villars representation      31ff 72
Feshbach, Herman      98
Feynman dagger notation      129
Feynman, Richard Phillips      148
Field operator, quantized      321
Field strength tensor      255
Fierz — Pauli — Gupta form      387
Fierz, Markus      388
Fine-structure constant      45 225 296
Fine-structure splitting      290
Fine-structure splitting, relativistic      275
Foldy — Wouthuysen representation      277ff
Form factor      89
Form invariance      66
Forward-scattering amplitude      94
Four-current density      103 148
Four-current density of charge of the Klein — Gordon equation      8
Four-current of the Klein — Gordon equation      5
Four-gradient      2
Four-momentum      2
Four-momentum, operator      3
Four-potential      2
Four-vector      2
Free Dirac waves      111
Free solutions of the Dirac equations, energies of      111
Free solutions of the Dirac equations, normalization of      108
Free solutions of the Dirac equations, positive/negative energy      108
Free-pion Hamiltonian      86
Gauge invariance      41 49
Gauge invariance of the Klein — Gordon equation with minimal coupling      50
Gauge transformation      49
Gauge, Lorentz      365
Gauge, radiation      365
Gauge-invariant derivation      382
Gauss's theorem      18 93
Generalized Clebsch — Gordan theorem      414
Generators      391
Generators of O(3)      395
Generators of O(4) group transformations      391
Generators of the infinitesimal translations      399
Generators of the orthogonal group O(4)      392
Generators of the three-dimensional subgroup of O(4)      394
Generators, matrix representation of      392
Gordon decomposition      184ff
Gordon, Walter      97
Green's function      85 96
Green's operators      84
Ground-state energy of hydrogen      298
Group velocity, classical      184
Group, abelian      399
Group, conformal      400
Group, connected      396
Group, L      398
Group, O(3)      389ff
Group, O(3, 1)      390ff
Group, O(3, C)      390ff
Group, O(3, R)      390ff
Group, O(4)      390ff
Group, O(4, C)      390ff
Group, O(4, R)      390ff
Group, P      398ff
Group, SL(2, C)      406ff
Group, SO(4)      398ff
Group, SO(4, R)      397ff
Group, SU(2)      405
Group, SU(2, C)      403ff

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