Quantum Mechanics: An Introduction, 4/e

Quantum Mechanics - An Introduction lays the foundations for the rest of the course on quantum mechanics, advanced quantum mechanics and field theory. Starting from black-body radiation, the photoelectric effect, and wave-particle duality, Greiner goes on to discuss the uncertainty relations, spin, and many-body systems; he includes applications to the hydrogen atom and the Stern-Gerlach and Einstein-de Haas experiments. The mathematics of representation theory, S matrices, perturbation theory, eigenvalue problems, and hypergeometric differential equations are presented in detail, with 88 fully and carefully worked examples and exercises to consolidate the material. The book supplies the historical and phenomenological background and steadily builds a wave-mechanical treatment of matter. This fourth edition includes improved explanatory remarks, plus several new examples and exercises

Written for:


US: Advanced undergraduates + graduates (physics) RoW: Undergraduates 3rd year (physics)

Contents

1. The Quantization of Physical Quantities 1
1.1 Light Quanta 1
1.2 The Photoelectric Effect 1
1.3 The Compton Effect 2
1.4 The Ritz Combination Principle 4
1.5 The Franck­Hertz Experiment 4
1.6 The Stern­Gerlach Experiment 5
1.7 Biographical Notes 5
2. The Radiation Laws 9
2.1 A Preview of the Radiation of Bodies 9
2.2 What is Cavity Radiation? 10
2.3 The Rayleigh­Jeans Radiation Law: The Electromagnetic Eigenmodes of a Cavity 14
2.4 Planck's Radiation Law 16
2.5 Biographical Notes 26
3. Wave Aspects of Matter 29
3.1 De Broglie Waves 29
3.2 The Diffraction of Matter Waves 34
3.3 The Statistical Interpretation of Matter Waves 38
3.4 Mean (Expectation) Values in Quantum Mechanics 43
3.5 Three Quantum Mechanical Operators 46
3.6 The Superposition Principle in Quantum Mechanics 48
3.7 The Heisenberg Uncertainty Principle 51
3.8 Biographical Notes 65
4. Mathematical Foundations of Quantum Mechanics I 67
4.1 Properties of Operators 67
4.2 Combining Two Operators 68
4.3 Bra and Ket Notation 69
4.4 Eigenvalues and Eigenfunctions 70
4.5 Measurability of Different Observables at Equal Times 76
4.6 Position and Momentum Operators 78
4.7 Heisenberg's Uncertainty Relations for Arbitrary Observables 79
4.8 Angular-Momentum Operators 81
4.9 Kinetic Energy 85
4.10 Total Energy 85
4.11 Biographical Notes 103
5. Mathematical Supplement 105
5.1 Eigendifferentials and the Normalization of Eigenfunctions for Continuous Spectra 105
5.2 Expansion into Eigenfunctions 108
6. The Schrödinger Equation 117
6.1 The Conservation of Particle Number in Quantum Mechanics 144
6.2 Stationary States 146
6.3 Properties of Stationary States 147
6.4 Biographical Notes 154
7. The Harmonic Oscillator 157
7.1 The Solution of the Oscillator Equation 163
7.2 The Description of the Harmonic Oscillator by Creation and Annihilation Operators 173
7.3 Properties of the Operators â and â^+ 174
7.4 Representation of the Oscillator Hamiltonian in Terms of â and â^+ 175
7.5 Interpretation of â and â^^+ 176
7.6 Biographical Notes 182
8. The Transition from Classical to Quantum Mechanics 185
8.1 Motion of the Mean Values 185
8.2 Ehrenfest's Theorem 186
8.3 Constants of Motion, Laws of Conservation 187
8.4 Quantization in Curvilinear Coordinates 190
8.5 Biographical Notes 203
9. Charged Particles in Magnetic Fields 205
9.1 Coupling to the Electromagnetic Field 205
9.2 The Hydrogen Atom 217
9.3 Three-Dimensional Electron Densities 223
9.4 The Spectrum of Hydrogen Atoms 226
9.5 Currents in the Hydrogen Atom 228
9.6 The Magnetic Moment 229
9.7 Hydrogen-like Atoms 230
9.8 Biographical Notes 244
10. The Mathematical Foundations of Quantum Mechanics II 247
10.1 Representation Theory 247
10.2 Representation of Operators 251
10.3 The Eigenvalue Problem 260
10.4 Unitary Transformations 262
10.5 The S Matrix 264
10.6 The Schrödinger Equation in Matrix Form 266
10.7 The Schrödinger Representation 269
10.8 The Heisenberg Representation 269
10.9 The Interaction Representation 270
10.10 Biographical Notes 271
11. Perturbation Theory 273
11.1 Stationary Perturbation Theory 273
11.2 Degeneracy 277
11.3 The Ritz Variational Method 292
11.4 Time-Dependent Perturbation Theory 295
11.5 Time-Independent Perturbation 300
11.6 Transitions Between Continuum States 302
11.7 Biographical Notes 327
12. Spin 329
12.1 Doublet Splitting 330
12.2 The Einstein­de Haas Experiment 332
12.3 The Mathematical Description of Spin 333
12.4 Wave Functions with Spin 336
12.5 The Pauli Equation 339
12.6 Biographical Notes 352
13. A Nonrelativistic Wave Equation with Spin 355
13.1 The Linearization of the Schrödinger Equation 355
13.2 Particles in an External Field and the Magnetic Moment 363
14. Elementary Aspects of the Quantum-Mechanical Many-Body Problem 367
14.1 The Conservation of the Total Momentum of a Particle System 371
14.2 Centre-of-Mass Motion of a System of Particles in Quantum Mechanics 373
14.3 Conservation of Total Angular Momentum in a Quantum-Mechanical Many-Particle System 377
14.4 Small Oscillations in a Many-Particle System 390
14.5 Biographical Notes 401
15. Identical Particles 403
15.1 The Pauli Principle 405
15.2 Exchange Degeneracy 405
15.3 The Slater Determinant 407
15.4 Biographical Notes 421
16. The Formal Framework of Quantum Mechanics 423
16.1 The Mathematical Foundation of Quantum Mechanics: Hilbert Space 423
16.2 Operators in Hilbert Space 426
16.3 Eigenvalues and Eigenvectors 427
16.4 Operators with Continuous or Discrete-Continuous (Mixed) Spectra 431
16.5 Operator Functions 433
16.6 Unitary Transformations 436
16.7 The Direct-Product Space 437
16.8 The Axioms of Quantum Mechanics 438
16.9 Free Particles 441
16.10 A Summary of Perturbation Theory 455
17. Conceptual and Philosophical Problems of Quantum Mechanics 459
17.1 Determinism 459
17.2 Locality 460
17.3 Hidden-Variable Theories 462
17.4 Bell's Theorem 465
17.5 Measurement Theory 468
17.6 Schrödinger's Cat 471
17.7 Subjective Theories 472
17.8 Classical Measurements 472
17.9 The Copenhagen Interpretation 473
17.10 Indelible Recording 474
17.11 The Splitting Universe 476
17.12 The Problem of Reality 477
Subject Index 479
END