Preface ...................................................... XIII
1 Nonstationary Perturbations .................................. 1
1.1 Transition Probability .................................. 1
1.2 Perturbative Solution ................................... 2
1.3 Formal Series ........................................... 5
1.4 Adiabatic Perturbations ................................. 7
1.5 Adiabatic Perturbation Theory ........................... 8
1.6 Nonadiabatic Transitions ............................... 10
1.7 Geometric Phase ........................................ 13
1.8 Sudden Perturbations ................................... 16
1.9 Shake-Off Processes .................................... 19
2 Periodic Perturbations ...................................... 23
2.1 Golden Rule ............................................ 23
2.2 Beyond the First Order ................................. 26
2.3 Degenerate States ...................................... 26
2.4 Quasienergy ............................................ 28
2.5 Final States in the Continuum .......................... 29
2.6 Rotating Wave Approximation ............................ 35
2.7 Interaction with the Quantized Field ................... 38
2.8 Dressed States ......................................... 41
2.9 Super-Radiance ......................................... 42
3 Scattering of Fast Charged Particles ........................ 47
3.1 Scattering and Cross Section ........................... 47
3.2 Rutherford Scattering .................................. 49
3.3 Static Form-Factor ..................................... 51
3.4 Screening .............................................. 54
3.5 Atomic Excitation and Ionization ....................... 56
3.6 Energy Losses .......................................... 58
3.7 Coulomb Excitation ..................................... 60
4 Photons ..................................................... 63
4.1 Introduction: Classical and Quantum Field .............. 63
4.2 Hamiltonian Description of the Radiation Field ......... 64
4.3 Quantization of the Radiation Field .................... 67
4.4 Photon Wave Function ................................... 71
4.5 Vector Spherical Harmonics ............................. 73
4.6 Casimir Effect ......................................... 75
4.7 Euler-Maclaurin Summation Formula ...................... 77
4.8 Lamb Shift ............................................. 79
4.9 Interaction of Radiation with Matter ................... 82
5 Photoabsorption and Photoemission ........................... 87
5.1 Einstein Coefficients; Masers and Lasers ............... 87
5.2 Photoabsorption ........................................ 91
5.3 Long Wavelength Limit .................................. 92
5.4 Higher Multipole Transitions ........................... 95
5.5 Stimulated and Spontaneous Radiation ................... 97
5.6 Dipole Radiation ....................................... 98
5.7 Selection Rules and Examples .......................... 100
5.8 Photoelectric Effect .................................. 103
6 Dispersion and the Scattering of Light ..................... 107
6.1 Macroscopic Description ............................... 107
6.2 Linear Response ....................................... 108
6.3 Causality ............................................. 110
6.4 Dielectric Function ................................... 112
6.5 Dispersion Properties ................................. 114
6.6 Quantum Damping ....................................... 116
6.7 Dispersion Relations .................................. 118
6.8 Description of Scattering ............................. 119
6.9 Scattering Cross Section .............................. 121
6.10 Coherent Scattering ................................... 123
6.11 Resonance Fluorescence ................................ 124
6.12 Scattering off Many Centers ........................... 125
7 Basics of Quantum Scattering ............................... 129
7.1 Scattering and Observables ............................ 129
7.2 Classical Scattering and Cross Section ................ 130
7.3 Scattering Matrix ..................................... 133
7.4 Transition Rate ....................................... 134
7.5 Born Approximation .................................... 136
7.6 Continuity Equation ................................... 138
7.7 Elastic Scattering .................................... 139
7.8 Unitarity and Optical Theorem ......................... 140
7.9 Green Function ........................................ 142
7.10 Born Series ........................................... 145
7.11 Validity of the Born Approximation .................... 148
7.12 Scattering at High Energies ........................... 150
11 Towards Relativistic Quantum Mechanics ..................... 225
11.1 Limitations of the Approach .......................... 225
11.2 Relativistic Units ................................... 226
11.3 Lorentz Transformation ............................... 226
11.4 Energy and Momentum .................................. 227
11.5 Tensors and Notations ................................ 229
11.6 Klein-Gordon Equation ................................ 231
11.7 Current Conservation ................................. 233
11.8 Particles and Antiparticles .......................... 234
11.9 Electromagnetic Field ................................ 236
11.10 Minimal Electromagnetic Coupling ..................... 237
11.11 Photoabsorption at Higher Energies ................... 240
11.12 Nuclear Photoeffect .................................. 242
11.13 Estimates of Processes in QED ........................ 244
12 Dirac Equation: Formalism .................................. 249
12.1 Introducing the Dirac Equation ........................ 249
12.2 Covariant Form and Algebra ............................ 251
12.3 Current ............................................... 253
12.4 Charge Conjugation .................................... 254
12.5 Relativistic Transformations .......................... 256
12.6 Spin Operator ......................................... 258
12.7 Bilinear Covariants ................................... 260
13 Dirac Equation: Solutions .................................. 265
13.1 Free Motion ........................................... 265
13.2 Dirac Sea ............................................. 266
13.3 Explicit Solutions .................................... 267
13.4 Complete Set of Solutions ............................. 270
13.5 Pauli Equation ........................................ 273
13.6 Second Order Effects .................................. 274
13.7 Central Field ......................................... 276
13.8 Coulomb Field ......................................... 279
13.9 Static Uniform Magnetic Field ......................... 283
14 Discrete Symmetries, Neutrino and Kaons .................... 285
14.1 Parity Transformation for a Dirac Particle ............ 285
14.2 Time-Reversal Transformation .......................... 287
14.3 CVT Transformation .................................... 288
14.4 Massless Particles .................................... 289
14.5 Neutrinos in the Massless Limit ....................... 291
14.6 Parity Non-conservation Revisited ..................... 293
14.7 Neutrino Oscillations ................................. 295
14.8 Majorana Neutrinos .................................... 297
14.9 Strangeness ........................................... 299
14.10 Neutral Kaons and CP-parity .......................... 300
14.11 Neutral Kaons and Quantum Regeneration ............... 303
15 Identical Particles ........................................ 307
15.1 Indistinguishable Particles ........................... 307
15.2 Permutational Symmetry ................................ 308
15.3 Bosons and Fermions ................................... 310
15.4 Wave Functions of Noninteracting Particles ............ 312
15.5 Two-Nucleon States .................................... 315
15.6 Scattering of Identical Particles ..................... 324
15.7 Intensity Interferometry .............................. 328
16 Isospin .................................................... 331
16.1 Introducing Isospin ................................... 331
16.2 Isospin Invariance .................................... 333
16.3 Isospin of Many-Body Systems .......................... 334
16.4 Isospin and Space-Spin Symmetry ....................... 336
16.5 A Glimpse of a More General Picture ................... 338
16.6 Relations between Cross Sections ...................... 340
17 Secondary Quantization ..................................... 345
17.1 Occupation Number Representation ...................... 345
17.2 Introduction to Secondary Quantization ................ 347
17.3 Bose-Statistics ....................................... 348
17.4 Fermi-Statistics ...................................... 350
17.5 Algebraic Relations ................................... 351
17.6 One-Body Operators .................................... 352
17.7 Two-Body Operators .................................... 356
17.8 Interparticle Interaction in the Plane-Wave Basis ..... 357
17.9 Interparticle Interaction in a Finite System .......... 359
18 Atomic and Nuclear Configurations .......................... 363
18.1 Independent Particle Approximation .................... 363
18.2 Adding Rotational Invariance .......................... 364
18.3 Many-Particle Configurations .......................... 366
18.4 Exchange Interaction .................................. 370
18.5 Two-Electron System ................................... 372
18.6 Helium Atom: Optical Spectrum ......................... 375
18.7 Hund's Rules .......................................... 376
18.8 Particle-Hole Symmetry ................................ 378
18.9 Shell Structure ....................................... 380
19 Fermions ................................................... 383
19.1 Ideal Fermi-Gas ....................................... 383
19.2 Spin Paramagnetism .................................... 388
19.3 Orbital Diamagnetism .................................. 391
19.4 Introducing Mean Field ................................ 393
19.5 Statistical Model ..................................... 395
19.6 Screening in the Electron Gas ......................... 398
19.7 Hartree-Fock Approximation ............................ 399
19.8 Spatially Uniform System .............................. 402
19.9 Coulomb Gas ........................................... 404
19.10 Density Functional Theory ............................ 406
20 Collective Excitations ..................................... 409
20.1 Linear Chain .......................................... 409
20.2 Phonons ............................................... 413
20.3 Phonon Modes .......................................... 415
20.4 Spin Waves ............................................ 418
20.5 Particle-Hole Excitations ............................. 424
20.6 Density Fluctuations .................................. 426
20.7 Random Phase Approximation ............................ 428
20.8 Electron-Phonon Interaction ........................... 429
21 Bosons ..................................................... 433
21.1 Bose-Einstein Condensation ............................ 433
21.2 Condensate as a Reservoir; Chemical Potential ......... 435
21.3 Weakly Non-ideal Gas .................................. 437
21.4 Phonons ............................................... 439
21.5 Superfluidity ......................................... 441
21.6 Canonical Transformation .............................. 442
21.7 Phonons as Density Waves .............................. 445
21.8 Local Density Approximation ........................... 447
21.9 Non-uniform Gas ....................................... 450
22 Fermion Pairing and Superconductivity ...................... 453
22.1 Pairing ............................................... 453
22.2 Pairs and Seniority ................................... 455
22.3 Multipole Moments in the Seniority Scheme ............. 458
22.4 Degenerate Model and Quasispin ........................ 459
22.5 Canonical Transformation .............................. 462
22.6 BCS Theory and Trial Wave Function .................... 466
22.7 Energy Minimization ................................... 467
22.8 Energy Gap ............................................ 469
22.9 Excitation Spectrum ................................... 473
22.10 Condensation Energy .................................. 477
22.11 Transition Amplitudes ................................ 478
23 Density Matrix ............................................. 481
23.1 Mixed States and Density Matrix ....................... 481
23.2 Properties of the Density Matrix ...................... 482
23.3 Thermal Equilibrium ................................... 486
23.4 Polarization Density Matrix ........................... 489
23.5 Application of Scattering ............................. 493
23.6 Ensemble Entropy ...................................... 496
23.7 Evolution of the Density Matrix ....................... 498
23.8 Linear Response Revisited ............................. 500
23.9 Electric Conductivity ................................. 501
24 Quantum Chaos .............................................. 505
24.1 Classical and Quantum Chaos ........................... 505
24.2 Local Spectral Statistics: Poisson Distribution ....... 508
24.3 Gaussian Orthogonal Ensemble .......................... 512
24.4 Level Spacing Distribution ............................ 514
24.5 GOE and Information ................................... 517
24.6 Universality Classes .................................. 518
24.7 Semicircle Law ........................................ 521
24.8 Chaotic Eigenfunctions ................................ 527
24.9 Complexity and Information Entropy .................... 531
24.10 Porter-Thomas and Related Distributions .............. 533
25 Quantum Entanglement ....................................... 535
25.1 Entanglement .......................................... 535
25.2 Teleportation ......................................... 536
25.3 Mathematics of Entanglement ........................... 538
25.4 Quantum Bell Inequalities ............................. 541
25.5 EPR(B) Paradox and Hidden Variables ................... 543
25.6 Experimental Tests .................................... 546
25.7 Decoherence and Measurement Paradox ................... 547
References ................................................. 551
Further Reading ............................................ 555
Index ......................................................... 563
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