Quantum Physics, Volume 1: From Basics to Symmetries and Perturbations

Zelevinsky, V.Quantum physics vol.1 From Basics to Symmetries and Perturbations (Wiley-VCH,2011)(ISBN 9783527409792)(600dpi)(617p)......Page 4
Copyright iv ......Page 5
Contents v ......Page 6
Preface xiii  ......Page 13
1.1 Light: Waves or Particles? 1 ......Page 15
1.2 Planck Constant, Beginning of the Quantum Era 2 ......Page 16
1.3 Photons 3 ......Page 17
1.4 Spectroscopy and Stability of Atoms 5 ......Page 19
1.5 Bohr Postulates 6 ......Page 20
1.6 Hydrogen Atom 9 ......Page 23
1.7 Correspondence Principle 15 ......Page 29
1.8 Spatial Quantization 18 ......Page 32
1.9 Spin 20 ......Page 34
1.10 De Broglie Waves 21 ......Page 35
2.1 Free Motion 25 ......Page 39
2.2 Probability Density and Current 26 ......Page 40
2.3 Superposition Principle and Uncertainty 29 ......Page 43
2.4 Potential Wall 30 ......Page 44
2.5 Potential Barrier 31 ......Page 45
2.6 Barrier Penetration 35 ......Page 49
2.7 Tunneling 36 ......Page 50
3.1 Potential Box 43 ......Page 57
3.2 Orthogonality and Completeness 45 ......Page 59
3.3 Delta-Function* 46 ......Page 60
3.4 Time Evolution 49 ......Page 63
3.5 Shallow Well and Quantum Halo 52 ......Page 66
3.6 Resonances 59 ......Page 73
3.7 Level Density 60 ......Page 74
3.8 Periodic Boundary Conditions 62 ......Page 76
3.9 Counting Levels in a Smooth Potential 63 ......Page 77
4.1 Momentum Representation 67 ......Page 81
4.2 Introducing Operators 70 ......Page 84
4.3 Commutators 72 ......Page 86
4.4 Eigenfunctions and Eigenvalues 74 ......Page 88
4.5 Momentum as a Translation Generator 75 ......Page 89
4.6 Introduction to Groups* 78 ......Page 92
4.7 Orbital Momentum as a Rotation Generator 79 ......Page 93
4.8 Transformation of Operators 81 ......Page 95
5.1 Uncertainty in Wave Mechanics 85 ......Page 99
5.2 Simple Examples 87 ......Page 101
5.3 Complementarity and Probability 91 ......Page 105
5.4 Wave Packet: Propagation 94 ......Page 109
5.5 Spreading of a Wave Packet 96 ......Page 110
5.6 Estimates with Uncertainty Relations 100 ......Page 114
5.7 Classification of Molecular Excitations 104 ......Page 118
5.8 Level Width 107 ......Page 121
5.9 Line Width and Mossbauer Effect 109 ......Page 123
5.10 Virtual Processes and Relativistic Effects 112 ......Page 126
5.11 Spatial Quantization Revisited 114 ......Page 128
6.1 Probability Amplitude 119 ......Page 133
6.2 Superposition and Interference 120 ......Page 134
6.3 State Vectors 123 ......Page 137
6.4 Geometry of Hilbert Space* 124 ......Page 138
6.5 Linear Operators* 128 ......Page 142
6.6 Hermitian Operators* 130 ......Page 144
6.7 Properties of Hermitian Operators* 132 ......Page 146
6.8 Diagonalization* 134 ......Page 148
6.9 Basis Transformations* 136 ......Page 150
6.10 Continuous Transformations and Generators* 138 ......Page 152
6.11 Projection Operators* 140 ......Page 154
6.12 Operators of Observables 142 ......Page 156
6.13 Simultaneous Measurability 144 ......Page 158
6.14 Quantifying Uncertainty Relations 146 ......Page 160
7.1 Hamiltonian and Schrodinger Equation 153 ......Page 167
7.2 Single-Particle Hamiltonian 155 ......Page 169
7.3 Continuity Equation 161 ......Page 175
7.4 Wigner Distribution 165 ......Page 179
7.5 Heisenberg Picture 167 ......Page 181
7.6 Operator Dynamics 168 ......Page 182
7.7 Virial Theorem 171 ......Page 185
7.8 Survival Probability 173 ......Page 187
7.9 Sum Rules 174 ......Page 188
7.10 Conservation Laws 178 ......Page 192
7.11 Path Integral Formulation 180 ......Page 194
7.12 Relation to Classical Mechanics 183 ......Page 197
7.13 Back to the Schrodinger Picture 184 ......Page 198
8.1 Time-Reversal Invariance 187 ......Page 201
8.2 Time-Reversal Transformation of Operators 189 ......Page 203
8.3 Inversion and Parity 191 ......Page 205
8.4 Scalars and Pseudoscalars, Vectors and Pseudovectors 192 ......Page 206
8.5 Parity Conservation 193 ......Page 207
8.6 Symmetry of a Crystal Lattice 197 ......Page 211
8.7 Quasimomentum and Bloch Functions 198 ......Page 212
8.8 Energy Bands 201 ......Page 215
8.9 Symmetry of Molecules 203 ......Page 217
8.10 More Group Theory: Conjugate Classes* 206 ......Page 220
8.11 Group Representations* 207 ......Page 221
8.12 Orthogonality and Completeness* 209 ......Page 223
8.13 Characters* 212 ......Page 226
9.1 Eigenvalue Problem 217 ......Page 231
9.2 Continuous Spectrum 218 ......Page 232
9.3 Degeneracy in the Continuum 221 ......Page 235
9.4 Transfer Matrix 224 ......Page 238
9.5 Delay Time 225 ......Page 239
9.6 Uniform Field 228 ......Page 242
9.7 Airy and Bessel Functions* 229 ......Page 243
9.8 Asymptotic Behavior* 232 ......Page 246
9.9 Asymptotics of the Airy Function* 234 ......Page 248
9.10 Green Function for One-Dimensional Scattering 237 ......Page 251
9.11 Potential as Perturbation 241 ......Page 255
9.12 Quasistationary States 244 ......Page 258
10.1 Variational Principle 247 ......Page 261
10.2 Direct Variational Method 249 ......Page 263
10.3 Diagonalization in a Truncated Basis 251 ......Page 265
10.4 Two-State System 252 ......Page 266
10.5 Level Repulsion and Avoided Crossing 254 ......Page 268
10.6 Time Evolution of a Two-State System 257 ......Page 271
10.7 Bright State and Fragmentation 259 ......Page 273
10.8 Collective States 261 ......Page 275
10.9 Lanczos Algorithm 265 ......Page 279
11.1 One-Dimensional Bound States 267 ......Page 281
11.2 Linear Harmonic Oscillator 269 ......Page 283
11.3 Hermite Polynomials* 275 ......Page 289
11.4 Harmonic Oscillator in Plane: Separation of Variables 278 ......Page 292
11.5 Isotropic Oscillator 280 ......Page 294
11.6 Solving the Problem in Polar Coordinates 282 ......Page 296
11.7 Ladder Construction 285 ......Page 299
11.8 Creation and Annihilation Operators 286 ......Page 300
11.9 Operator Solution for the Harmonic Oscillator 288 ......Page 302
12.1 Introducing Coherent States 293 ......Page 307
12.2 Displacements in the Phase Plane 294 ......Page 308
12.3 Properties of Coherent States 296 ......Page 310
12.4 Coherent States of the Harmonic Oscillator 298 ......Page 312
12.5 Linear Source 299 ......Page 313
12.6 Semiclassical Limit, Number of Quanta and the Phase 302 ......Page 316
12.7 Pairwise Source 304 ......Page 318
12.8 Squeezed States 307 ......Page 321
12.9 More about Squeezed States 310 ......Page 324
13.1 Magnetic Field in Classical Mechanics 315 ......Page 329
13.2 Quantum Formulation and Gauge Invariance 317 ......Page 331
13.3 Are Electromagnetic Potentials Observable? 320 ......Page 334
13.4 Landau Levels: Energy Spectrum 321 ......Page 335
13.5 Landau Levels: Degeneracy and Wave Functions 323 ......Page 337
13.6 Quantum Hall Effect 327 ......Page 341
13.7 Arbitrary Dispersion Law 331 ......Page 345
13.8 Symmetric Gauge 335 ......Page 349
13.9 Coherent States in the Magnetic Field 336 ......Page 350
14.1 Ideas of Macroscopic Coherence 339 ......Page 353
14.2 Macroscopic Wave Function 340 ......Page 354
14.3 Hydrodynamic Description 341 ......Page 355
14.4 Dynamics of the Macroscopic Coherent State 344 ......Page 358
14.5 Josephson Effects 346 ......Page 360
14.6 Quantization of Circulation and Quantum Vortices 349 ......Page 363
14.7 Magnetic Fluxoid Quantization and London Electrodynamics 353 ......Page 367
15.1 Heuristic Introduction 357 ......Page 371
15.2 Semiclassical Approximation 360 ......Page 374
15.3 Asymptotic Expansion 363 ......Page 377
15.4 Stationary Phase 364 ......Page 378
15.5 Matching Conditions 365 ......Page 379
15.6 Bohr-Sommerfeld Quantization 369 ......Page 383
15.7 Semiclassical Matrix Elements 371 ......Page 385
15.8 Solutions in the Complex Plane* 373 ......Page 387
15.9 Going Around the Complex Plane* 376 ......Page 390
15.10 Connection Formulae Revisited* 378 ......Page 392
15.11 Close Turning Points* 379 ......Page 393
15.12 Path Integral Approach 383 ......Page 397
16.1 Angular Momentum as a Generator of Rotations 387 ......Page 401
16.2 Spin 389 ......Page 403
16.3 Angular Momentum Multiplets 390 ......Page 404
16.4 Matrix Elements of Angular Momentum 396 ......Page 410
16.5 Realization of the Algebra for Orbital Momentum 399 ......Page 413
16.6 Constructing a Set of Spherical Functions* 401 ......Page 415
16.7 Simplest Properties of Spherical Functions* 403 ......Page 417
16.8 Scalars and Vectors* 404 ......Page 418
16.9 Second Rank Tensors* 408 ......Page 422
16.10 Spherical Functions and Legendre Polynomials* 410 ......Page 424
16.11 Angular Momentum in an External Field 414 ......Page 428
17.1 Reduction to the One-Body Problem 417 ......Page 431
17.2 Separation of Angular Variables 420 ......Page 434
17.3 Radial Part of the Schrodinger Equation 422 ......Page 436
17.4 Free Motion 426 ......Page 440
17.5 Plane and Spherical Waves 430 ......Page 444
17.6 Spherical Well 432 ......Page 446
17.7 Short-Range Potential 435 ......Page 449
17.8 Adding the Second Center 436 ......Page 450
17.9 Three-Dimensional Harmonic Oscillator 439 ......Page 453
18.1 Bound States 445 ......Page 459
18.2 Ground State 447 ......Page 461
18.3 Discrete Spectrum 450 ......Page 464
18.4 Operator Solution 458 ......Page 472
18.5 On the Way to Precision Spectroscopy 460 ......Page 474
18.6 Solution in Parabolic Coordinates* 462 ......Page 476
18.7 Continuum States 463 ......Page 477
19 Stationary Perturbations 469 ......Page 483
19.1 Introduction 469 ......Page 484
19.2 Perturbation Theory With No Degeneracy 470 ......Page 485
19.3 Convergence 474 ......Page 489
19.4 Case of Close Levels 477 ......Page 491
19.5 Adiabatic Approximation 478 ......Page 492
19.6 Molecular Ion of Hydrogen 482 ......Page 496
19.7 Interactions of Atoms at Large Distances 486 ......Page 500
20.1 SU(2) Group 489 ......Page 503
20.2 Spin 1/2: Algebra 490 ......Page 504
20.3 Spinors 494 ......Page 508
20.4 Magnetic Resonance 499 ......Page 513
20.5 Time-Reversal Transformation and Kramers Theorem 501 ......Page 515
20.6 Time-Conjugate States 503 ......Page 517
20.7 Spinors as Qubits 504 ......Page 518
21.1 Matrices of Finite Rotations 509 ......Page 523
21.2 Spherical Functions as Matrix Elements of Finite Rotations 511......Page 525
21.3 Addition Theorem* 514 ......Page 528
21.4 Transformation of Operators 516 ......Page 530
21.5 Introduction to Selection Rules 518 ......Page 532
21.6 Electromagnetic Multipoles 519 ......Page 533
22.1 Two Subsystems 523 ......Page 537
22.2 Decomposition of Reducible Representations 525 ......Page 539
22.3 Two Particles of Spin 1/2 528 ......Page 542
22.4 Tensor Operators and Selection Rules Revisited 532 ......Page 546
22.5 Applying to Electromagnetic Multipoles 533 ......Page 547
22.6 Vector Coupling of Angular Momenta 534 ......Page 548
22.7 Wigner-Eckart Theorem 538 ......Page 552
22.8 Vector Model 539 ......Page 553
22.9 Electric Dipole Moment and Anapole Moment 541 ......Page 555
22.10 Clebsch-Gordan Series* 543 ......Page 557
23.1 Spin-Orbit Coupling 545 ......Page 559
23.2 Spin-Orbit Splitting 547 ......Page 561
23.3 Hydrogen Fine Structure 550 ......Page 564
23.4 Fine Structure in Complex Atoms 553 ......Page 567
23.5 Magnetic Moment with Spin-Orbit Coupling 555 ......Page 569
23.6 Magnetic Hyperfine Structure 558 ......Page 572
23.7 Example: One Valence Electron 560 ......Page 574
23.8 Quadrupole Hyperfine Structure 562 ......Page 576
24.1 Polarizability in a Static Electric Field 567 ......Page 581
24.2 Stark Effect 569 ......Page 583
24.3 Polarizability of the Hydrogen Atom 570 ......Page 584
24.4 Stark Effect in the Hydrogen Atom 572 ......Page 586
24.5 Non-uniform Electric Field and Additional Comments 573 ......Page 587
24.6 Classical Zeeman Effect 574 ......Page 588
24.7 A Quantum System in a Magnetic Field 575 ......Page 589
24.8 Normal Quantum Zeeman Effect 576 ......Page 590
24.9 Anomalous Quantum Zeeman Effect 578 ......Page 592
24.10 Stronger Magnetic Field 579 ......Page 593
24.11 Diamagnetism 581 ......Page 595
24.12 Towards Really Strong Magnetic Fields 583 References 587 ......Page 601
Further Readings 591 ......Page 605
Index 597 ......Page 611
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