Zelevinsky V. Quantum physics; vol.1: From basics to symmetries and perturbations (Weinheim, 2011). - ОГЛАВЛЕНИЕ / CONTENTS
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ОбложкаZelevinsky V. Quantum physics. Vol.1: From basics to symmetries and perturbations. - Weinheim: Wiley-VCH, 2011. - xiv, 602 p. - Ref.: p.587-589. - Ind.: p.597-602. - ISBN 978-3-527-40979-2
 

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Оглавление / Contents
 
Preface ...................................................... XIII

1  Origin of Main Quantum Concepts .............................. 1
   1.1  Light: Waves or Particles? .............................. 1
   1.2  Planck Constant, Beginning of the Quantum Era ........... 2
   1.3  Photons ................................................. 3
   1.4  Spectroscopy and Stability of Atoms ..................... 5
   1.5  Bohr Postulates ......................................... 6
   1.6  Hydrogen Atom ........................................... 9
   1.7  Correspondence Principle ............................... 15
   1.8  Spatial Quantization ................................... 18
   1.9  Spin ................................................... 20
   1.10 De Broglie Waves ....................................... 21
2  Wave Function and the Simplest Problems ..................... 25
   2.1  Free Motion ............................................ 25
   2.2  Probability Density and Current ........................ 26
   2.3  Superposition Principle and Uncertainty ................ 29
   2.4  Potential Wall ......................................... 30
   2.5  Potential Barrier ...................................... 31
   2.6  Barrier Penetration .................................... 35
   2.7  Tunneling .............................................. 36
3  Bound States ................................................ 43
   3.1  Potential Box .......................................... 43
   3.2  Orthogonality and Completeness ......................... 45
   3.3  Delta-Function* ........................................ 46
   3.4  Time Evolution ......................................... 49
   3.5  Shallow Well and Quantum Halo .......................... 52
   3.6  Resonances ............................................. 59
   3.7  Level Density .......................................... 60
   3.8  Periodic Boundary Conditions ........................... 62
   3.9  Counting Levels in a Smooth Potential .................. 63
4  Dynamical Variables ......................................... 67
   4.1  Momentum Representation ................................ 67
   4.2  Introducing Operators .................................. 70
   4.3  Commutators ............................................ 72
   4.4  Eigenfunctions and Eigenvalues ......................... 74
   4.5  Momentum as a Translation Generator .................... 75
   4.6  Introduction to Groups ................................. 78
   4.7  Orbital Momentum as a Rotation Generator ............... 79
   4.8  Transformation of Operators ............................ 81
5  Uncertainty Relations ....................................... 85
   5.1  Uncertainty in Wave Mechanics .......................... 85
   5.2  Simple Examples ........................................ 87
   5.3  Complementarity and Probability ........................ 91
   5.4  Wave Packet: Propagation ............................... 94
   5.5  Spreading of a Wave Packet ............................. 96
   5.6  Estimates with Uncertainty Relations .................. 100
   5.7  Classification of Molecular Excitations ............... 104
   5.8  Level Width ........................................... 107
   5.9  Line Width and Mossbauer Effect ....................... 109
   5.10 Virtual Processes and Relativistic Effects ............ 112
   5.11 Spatial Quantization Revisited ........................ 114
6  Hilbert Space and Operators ................................ 119
   6.1  Probability Amplitude ................................. 119
   6.2  Superposition and Interference ........................ 120
   6.3  State Vectors ......................................... 123
   6.4  Geometry of Hilbert Space* ............................ 124
   6.5  Linear Operators* ..................................... 128
   6.6  Hermitian Operators* .................................. 130
   6.7  Properties of Hermitian Operators* .................... 132
   6.8  Diagonalization* ...................................... 134
   6.9  Basis Transformations* ................................ 136
   6.10 Continuous Transformations and Generators* ............ 138
   6.11 Projection Operators* ................................. 140
   6.12 Operators of Observables .............................. 142
   6.13 Simultaneous Measurability ............................ 144
   6.14 Quantifying Uncertainty Relations ..................... 146
7  Quantum Dynamics ........................................... 153
   7.1  Hamiltonian and Schrodinger Equation .................. 153
   7.2  Single-Particle Hamiltonian ........................... 155
   7.3  Continuity Equation ................................... 161
   7.4  Wigner Distribution ................................... 165
   7.5  Heisenberg Picture .................................... 167
   7.6  Operator Dynamics ..................................... 168
   7.7  Virial Theorem ........................................ 171
   7.8  Survival Probability .................................. 173
   7.9  Sum Rules ............................................. 174
   7.10 Conservation Laws ..................................... 178
   7.11 Path Integral Formulation ............................. 180
   7.12 Relation to Classical Mechanics ....................... 183
   7.13 Back to the Schrodinger Picture ....................... 184
8  Discrete Symmetries ........................................ 187
   8.1  Time-Reversal Invariance .............................. 187
   8.2  Time-Reversal Transformation of Operators ............. 189
   8.3  Inversion and Parity .................................. 191
   8.4  Scalars and Pseudoscalars, Vectors and
        Pseudovectors ......................................... 192
   8.5  Parity Conservation ................................... 193
   8.6  Symmetry of a Crystal Lattice ......................... 197
   8.7  Quasimomentum and Bloch Functions ..................... 198
   8.8  Energy Bands .......................................... 201
   8.9  Symmetry of Molecules ................................. 203
   8.10 More Group Theory: Conjugate Classes* ................. 206
   8.11 Group Representations* ................................ 207
   8.12 Orthogonality and Completeness* ....................... 209
   8.13 Characters* ........................................... 212
9  One-Dimensional Motion: Continuum .......................... 217
   9.1  Eigenvalue Problem .................................... 217
   9.2  Continuous Spectrum ................................... 218
   9.3  Degeneracy in the Continuum ........................... 221
   9.4  Transfer Matrix ....................................... 224
   9.5  Delay Time ............................................ 225
   9.6  Uniform Field ......................................... 228
   9.7  Airy and Bessel Functions* ............................ 229
   9.8  Asymptotic Behavior* .................................. 232
   9.9  Asymptotics of the Airy Function* ..................... 234
   9.10 Green Function for One-Dimensional Scattering ......... 237
   9.11 Potential as Perturbation ............................. 241
   9.12 Quasistationary States ................................ 244
10 Variational Approach and Diagonalization ................... 247
   10.1 Variational Principle ................................. 247
   10.2 Direct Variational Method ............................. 249
   10.3 Diagonalization in a Truncated Basis .................. 251
   10.4 Two-State System ...................................... 252
   10.5 Level Repulsion and Avoided Crossing .................. 254
   10.6 Time Evolution of a Two-State System .................. 257
   10.7 Bright State and Fragmentation ........................ 259
   10.8 Collective States ..................................... 261
   10.9 Lanczos Algorithm ..................................... 265
11 Discrete Spectrum and Harmonic Oscillator .................. 267
   11.1 One-Dimensional Bound States .......................... 267
   11.2 Linear Harmonic Oscillator ............................ 269
   11.3 Hermite Polynomials* .................................. 275
   11.4 Harmonic Oscillator in Plane: Separation of
        Variables ............................................. 278
   11.5 Isotropic Oscillator .................................. 280
   11.6 Solving the Problem in Polar Coordinates .............. 282
   11.7 Ladder Construction ................................... 285
   11.8 Creation and Annihilation Operators ................... 286
   11.9 Operator Solution for the Harmonic Oscillator ......... 288
12 Coherent and Squeezed States ............................... 293
   12.1 Introducing Coherent States ........................... 293
   12.2 Displacements in the Phase Plane ...................... 294
   12.3 Properties of Coherent States ......................... 296
   12.4 Coherent States of the Harmonic Oscillator ............ 298
   12.5 Linear Source ......................................... 299
   12.6 Semiclassical Limit, Number of Quanta and the Phase ... 302
   12.7 Pairwise Source ....................................... 304
   12.8 Squeezed States ....................................... 307
   12.9 More about Squeezed States............................. 310
13 Introducing Magnetic Field ................................. 315
   13.1 Magnetic Field in Classical Mechanics ................. 315
   13.2 Quantum Formulation and Gauge Invariance .............. 317
   13.3 Are Electromagnetic Potentials Observable? ............ 320
   13.4 Landau Levels: Energy Spectrum ........................ 321
   13.5 Landau Levels: Degeneracy and Wave Functions .......... 323
   13.6 Quantum Hall Effect ................................... 327
   13.7 Arbitrary Dispersion Law .............................. 331
   13.8 Symmetric Gauge ....................................... 335
   13.9 Coherent States in the Magnetic Field ................. 336
14 Macroscopic Quantum Coherence .............................. 339
   14.1 Ideas of Macroscopic Coherence ........................ 339
   14.2 Macroscopic Wave Function ............................. 340
   14.3 Hydrodynamic Description .............................. 341
   14.4 Dynamics of the Macroscopic Coherent State ............ 344
   14.5 Josephson Effects ..................................... 346
   14.6 Quantization of Circulation and Quantum Vortices ...... 349
   14.7 Magnetic Fluxoid Quantization and London
        Electrodynamics ....................................... 353
15 Semiclassical (WKB) Approximation .......................... 357
   15.1 Heuristic Introduction ................................ 357
   15.2 Semiclassical Approximation ........................... 360
   15.3 Asymptotic Expansion .................................. 363
   15.4 Stationary Phase ...................................... 364
   15.5 Matching Conditions ................................... 365
   15.6 Bohr-Sommerfeld Quantization .......................... 369
   15.7 Semiclassical Matrix Elements ......................... 371
   15.8 Solutions in the Complex Plane* ....................... 373
   15.9 Going Around the Complex Plane* ....................... 376
   15.10 Connection Formulae Revisited* ....................... 378
   15.11 Close Turning Points* ................................ 379
   15.12 Path Integral Approach ............................... 383
   16 Angular Momentum and Spherical Functions ................ 387
   16.1 Angular Momentum as a Generator of Rotations .......... 387
   16.2 Spin .................................................. 389
   16.3 Angular Momentum Multiplets ........................... 390
   16.4 Matrix Elements of Angular Momentum ................... 396
   16.5 Realization of the Algebra for Orbital Momentum ....... 399
   16.6 Constructing a Set of Spherical Functions* ............ 401
   16.7 Simplest Properties of Spherical Functions* ........... 403
   16.8 Scalars and Vectors* .................................. 404
   16.9 Second Rank Tensors* .................................. 408
   16.10 Spherical Functions and Legendre Polynomials* ........ 410
   16.11 Angular Momentum in an External Field ................ 414
17 Motion in a Central Field .................................. 417
   17.1 Reduction to the One-Body Problem ..................... 417
   17.2 Separation of Angular Variables ....................... 420
   17.3 Radial Part of the Schrodinger Equation ............... 422
   17.4 Free Motion ........................................... 426
   17.5 Plane and Spherical Waves ............................. 430
   17.6 Spherical Well ........................................ 432
   17.7 Short-Range Potential ................................. 435
   17.8 Adding the Second Center .............................. 436
   17.9 Three-Dimensional Harmonic Oscillator ................. 439
18 Hydrogen Atom .............................................. 445
   18.1 Bound States .......................................... 445
   18.2 Ground State .......................................... 447
   18.3 Discrete Spectrum ..................................... 450
   18.4 Operator Solution ..................................... 458
   18.5 On the Way to Precision Spectroscopy .................. 460
   18.6 Solution in Parabolic Coordinates* .................... 462
   18.7 Continuum States ...................................... 463
19 Stationary Perturbations ................................... 469
   19.1 Introduction .......................................... 469
   19.2 Perturbation Theory With No Degeneracy ................ 470
   19.1 Convergence ........................................... 474
   19.4 Case of Close Levels .................................. 477
   19.5 Adiabatic Approximation ............................... 478
   19.6 Molecular Ion of Hydrogen ............................. 482
   19.7 Interactions of Atoms at Large Distances .............. 486
20 Spin 1/2 ................................................... 489
   20.1 SU(2) Group ........................................... 489
   20.2 Spin 1/2: Algebra ..................................... 490
   20.3 Spinors ............................................... 494
   20.4 Magnetic Resonance .................................... 499
   20.5 Time-Reversal Transformation and Kramers Theorem ...... 501
   20.6 Time-Conjugate States ................................. 503
   20.7 Spinors as Qubits ..................................... 504
21 Finite Rotations and Tensor Operators ...................... 509
   21.1 Matrices of Finite Rotations .......................... 509
   21.2 Spherical Functions as Matrix Elements of Finite
        Rotations ............................................. 511
   21.3 Addition Theorem* ..................................... 514
   21.4 Transformation of Operators ........................... 516
   21.5 Introduction to Selection Rules ....................... 518
   21.6 Electromagnetic Multipoles ............................ 519
22 Angular Momentum Coupling .................................. 523
   22.1 Two Subsystems ........................................ 523
   22.2 Decomposition of Reducible Representations ............ 525
   22.3 Two Particles of Spin 1/2 ............................. 528
   22.4 Tensor Operators and Selection Rules Revisited ........ 532
   22.5 Applying to Electromagnetic Multipoles ................ 533
   22.6 Vector Coupling of Angular Momenta .................... 534
   22.7 Wigner-Eckart Theorem ................................. 538
   22.8 Vector Model .......................................... 539
   22.9 Electric Dipole Moment and Anapole Moment ............. 541
   22.10 Clebsch-Gordan Series* ............................... 543
   23 Fine and Hyperfine Structure ............................ 545
   23.1 Spin-Orbit Coupling ................................... 545
   23.2 Spin-Orbit Splitting .................................. 547
   23.3 Hydrogen Fine Structure ............................... 550
   23.4 Fine Structure in Complex Atoms ....................... 553
   23.5 Magnetic Moment with Spin-Orbit Coupling .............. 555
   23.6 Magnetic Hyperfine Structure .......................... 558
   23.7 Example: One Valence Electron ......................... 560
   23.8 Quadrupole Hyperfine Structure ........................ 562
   24 Atom in a Static Field .................................. 567
   24.1 Polarizability in a Static Electric Field ............. 567
   24.2 Stark Effect .......................................... 569
   24.3 Polarizability of the Hydrogen Atom ................... 570
   24.4 Stark Effect in the Hydrogen Atom ..................... 572
   24.5 Non-uniform Electric Field and Additional Comments .... 573
   24.6 Classical Zeeman Effect ............................... 574
   24.7 A Quantum System in a Magnetic Field .................. 575
   24.8 Normal Quantum Zeeman Effect .......................... 576
   24.9 Anomalous Quantum Zeeman Effect ....................... 578
   24.10 Stronger Magnetic Field .............................. 579
   24.11 Diamagnetism ......................................... 581
   24.12 Towards Really Strong Magnetic Fields ................ 583
   References ................................................. 587
   Further Readings ........................................... 591

Index ......................................................... 597


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