Verfügbarkeit: Quantum mechanics | Technische Universität München

Quantum mechanics: fundamentals

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Bibliographische Detailangaben
Beteiligte Personen:	Gottfried, Kurt 1929-2022 (VerfasserIn), Yan, Tung-Mow (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	New York, NY [u.a.] Springer 2004
Ausgabe:	2. ed., 1. softcover print.
Schlagwörter:	Mecânica quântica Quantentheorie Quantum theory Yan, Tung-mow Quantenmechanik
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012846110&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	XVII, 620 S.
ISBN:	0387220232 9780387220239

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Datensatz im Suchindex

DE-BY-TUM_call_number	0049 B.9.02.2003 A 217(2) 0102 PHY 020 2006 A 1426(2,2004)
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adam_text	Contents Preface vu Fundamental Concepts 1 1.1 Complementarity and Uncertainty ................... 1 (a) Complementarity 2 (b) The Uncertainty Principle 6 1.2 Superposition ............................... 11 (a) The Superposition Principle 11 (b) Two-Particle States 12 (c) Two-Particle Interferometry 1Ą (d) E PR Correlations 19 1.3 The Discovery of Quantum Mechanics ................. 20 1.4 Problems ................................. 24 The Formal Framework 27 2.1 The Formal Language: Hubert Space .................. 27 (a) Hubert Space 29 (b) Dirac s Notation 30 (c) Operators 32 (d) Unitary Transformations 35 (e) Eigenvalues and Eigenvectors 38 2.2 States and Probabilities ......................... 39 (a) Quantum States Ą0 (b) Measurement Outcomes A3 (c) Mixtures and the Density Matrix Ą6 (d) Entangled States 50 (e) The Wigner Distribution 52 2.3 Canonical Quantization ......................... 54 (a) The Canonical Commutation Rules 5Ą (b) Schrődinger Wave Functions 56 (c) Uncertainty Relations 59 2.4 The Equations of Motion ........................ 60 (a) The Schrődinger Picture 60 (b) The Heisenberg Picture 65 (c) Time Development of Expectation Values 66 (d) Time-Energy Uncertainty 67 (e) The Interaction Picture 70 2.5 Symmetries and Conservation Laws ................... 71 (a) Symmetries and Unitary Transformations 72 (b) Spatial Translations 73 xii Contents (c) Symmetry Groups 74 (d) Rotations 76 (e) Space Reflection and Parity 81 (f) Gauge Invariance 82 2.6 Propagators and Green s Functions ................... 84 (a) Propagators 8Ą (b) Green s Functions 85 (c) The Free Particle Propagator and Green s Function 87 (d) Perturbation Theory 89 2.7 The Path Integral ............................ 92 (a) The Feynman Path Integral 92 (b) The Free-Particle Path Integral 95 2.8 Semiclassical Quantum Mechanics ................... 98 (a) Hamilton- J acobi Theory 99 (b) The Semiclassical Wave Function 102 (c) The Semiclassical Propagator 104 (d) Derivations 106 2.9 Problems .................................109 Endnotes 111 3 Basic Tools 113 3.1 Angular Momentum: The Spectrum ..................113 3.2 Orbital Angular Momentum .......................116 3.3 Spin ....................................120 (a) Spin \| 121 (b) Spin 1 125 (c) Arbitrary Spins 127 3.4 Free-Particle States ............................128 3.5 Addition of Angular Momenta ......................133 (a) General Results 133 (b) Adding Spins j) and Unit Spins 135 (c) Arbitrary Angular Momenta; Clebsch-Gordan Coefficients 137 (d) Matrix Elements of Vector Operators 1Ą0 3.6 The Two-Body Problem .........................142 (a) Center-of-Mass and Relative Motion Ц2 (b) The Radial Schrödinger Equation: General Case Ц4 (c) Bound-State Coulomb Wave Functions 1Ą7 3.7 Basic Approximation Methods .....................149 (a) Stationary-State Perturbation Theory 150 (b) Degenerate-State Perturbation Theory 153 (c) Time-Dependent Perturbation Theory 156 (d) The Golden Rule 159 (e) The Variational Principle 161 3.8 Problems .................................162 4 Low-Dimensional Systems 165 4.1 Spectroscopy in Two-Level Systems ...................166 (a) Level Crossings 166 (b) Resonance Spectroscopy 169 Contents xiii 4.2 The Harmonic Oscillator .........................174 (a) Equations of Motion 17Ą (b) Energy Eigenvalues and Eigen) unctions 175 (c) The Forced Oscillator 178 (d) Coherent States 181 (e) Wigner Distributions 184 (f) Propagator and Path Integral 186 4.3 Motion in a Magnetic Field .......................188 (a) Equations of Motion and Energy Spectrum 188 (b) Eigenstates of Energy and Angular Momentum 190 (c) Coherent States 19Ą (d) The Aharonov-Bohm Effect 196 4.4 Scattering in One Dimension ......................198 (a) General Properties 198 (b) The Delta-Function Potential 202 (c) Resonant Transmission and Reflection 204 (d) The Exponential Decay Law 213 4.5 The Semiclassical Approximation ....................216 (a) The WKB Approximation 217 (b) Connection Formulas 218 (c) Energy Eigenvalues, Barrier Transmission, and ex-Decay 222 (d) Exactly Solvable Examples 225 4.6 Problems .................................228 Endnotes 233 Hydrogenic Atoms 235 5.1 Qualitative Overview ...........................235 5.2 The Kepler Problem ...........................238 (a) The Lenz Vector 238 (b) The Energy Spectrum 240 (c) The Conservation of M 242 (d) Wave Functions 243 5.3 Fine and Hyperfine Structure ......................245 (a) Fine Structure 245 (b) Hyperfine Structure — General Features 249 (c) Magnetic Dipole Hfs 250 (d) Electric Quadrupole Hfs 252 5.4 The Zeeman and Stark Effects .....................254 (a) Order of Magnitude Estimates 254 (b) The η = 2 Multiplet 257 (c) Strong Fields 260 5.5 Problems .................................263 Endnotes 266 Two-Electron Atoms 267 6.1 Two Identical Particles ..........................267 (a) Spin and Statistics 267 (b) The Exclusion Principle 269 (c) Symmetric and Antisymmetric States 270 ;iv Contents 6.2 The Spectrum of Helium .........................272 6.3 Atoms with Two Valence Electrons ...................275 (a) The Shell Model and Coupling Schemes 275 (b) The Configuration p2 276 6.4 Problems .................................279 Endnotes 281 7 Symmetries 283 7.1 Equivalent Descriptions and Wigner s Theorem ............283 7.2 Time Reversal ...............................286 (a) The Time Reversal Operator 287 (b) Spin 0 289 (c) Spin \| 290 7.3 Galileo Transformations .........................292 (a) Transformation of States: Galileo Invariance 292 (b) Mass Differences 295 7.4 The Rotation Group ...........................297 (a) The Group SO(3) 297 (b) SO(3) and SU{2) 299 (c) Irreducible Representations of SU{2) 301 (d) D(R) in Terms of Euler Angles 304 (e) The Kronecker Product 306 (f) Integration over Rotations 307 7.5 Some Consequences of Symmetry ....................311 (a) Rotation of Spherical Harmonics 312 (b) Helicity States ЗЦ (c) Decay Angular Distributions 316 (d) Rigid-Body Motion 317 7.6 Tensor Operators .............................320 (a) Definition of Tensor Operators 320 (b) The Wigner-Eckart Theorem 322 (c) Racah Coefficients and 6-j Symbols 32Ą 7.7 Geometric Phases .............................326 (a) Spin in Magnetic Field 327 (b) Correction to the Adiabatic Approximation 329 7.8 Problems .................................331 Endnotes 334 8 Elastic Scattering 335 8.1 Consequences of Probability and Angular Momentum Conservation . 335 (a) Partial Waves 335 (b) Hard Sphere Scattering З40 (c) Time-Dependent Description and the Optical Theorem З4О 8.2 General Properties of Elastic Amplitudes ...............345 (a) Integral Equations and the Scattering Amplitude 3Ą6 (b) A Solvable Example 350 (c) Bound-State Poles 353 (d) Symmetry Properties of the Amplitude 354 (e) Relations Between Laboratory and Center-of-Mass Quantities 356 Contents xv 8.3 Approximations to Elastic Amplitudes .................357 (a) The Born Approximation 358 (b) Validity of the Born Approximation 361 (c) Short-Wavelength Approximations 364 8.4 Scattering in a Coulomb Field ......................368 (a) The Coulomb Scattering Amplitude 368 (b) The Influence of a Short-Range Interaction 373 8.5 Scattering of Particles with Spin ....................376 (a) Symmetry Properties 377 (b) Cross Section and Spin Polarization 378 (c) Scattering of a Spin Particle by a Spin 0 Target 379 8.6 Neutron-Proton Scattering and the Deuteron.............382 (a) Low-Energy Neutron-Proton Scattering 383 (b) The Deuteron and Low-Energy np Scattering 385 (c) Neutron Scattering by the Hydrogen Molecule 388 (d) The Tensor Force 390 8.7 Scattering of Identical Particles .....................392 (a) Boson-Boson Scattering 392 (b) Fermion-Fermion Scattering 395 8.8 Problems .................................397 9 Inelastic Collisions 403 9.1 Atomic Collision Processes ........................403 (a) Scattering Amplitudes and Cross Sections ĄOĄ (b) Elastic Scattering 407 (c) Inelastic scattering Ą09 (d) Energy Loss 41% 9.2 The S Matrix ...............................414 (a) Scattering by a Bound Particle 415 (b) The S Matrix 417 (c) Transition Rates and Cross Sections 4%1 9.3 Inelastic Resonances ...........................424 (a) A Solvable Model 424 (b) Elastic and Inelastic Cross Sections 4%8 9.4 Problems .................................433 Endnotes 4З5 10 Electrodynamics 437 10.1 Quantization of the Free Field ......................437 (a) The Classical Theory 4З8 (b) Quantization 441 (c) Photons 44З (d) Space Reflection and Time Reversal 448 10.2 Causality and Uncertainty in Electrodynamics .............450 (a) Commutation Rides: Complementarity 450 (b) Uncertainty Relations 4^2 10.3 Vacuum Fluctuations ...........................454 (a) The Casimir Effect 455 (b) The Lamb Shift 458 xvi Contents 10.4 Radiative Transitions ...........................460 (a) The Interaction Between Field and Sources Ą61 (b) Transition Rates Ą63 (c) Dipole Transitions Ą66 10.5 Quantum Optics .............................468 (a) The Beam Splitter Ą68 (b) Various States of the Field Ą10 (c) Photon Coincidences Ą7Ą 10.6 The Photoeffect in Hydrogen ......................476 (a) High Energies Ą76 (b) The Cross Section Near Threshold 478 10.7 Scattering of Photons ..........................482 10.8 Resonant Scattering and Spontaneous Decay .............485 (a) Model Hamiltonian Ą86 (b) The Elastic Scattering Cross Section Ą88 (c) Decay of the Excited State 492 (d) The Connection Between Self-Energy and Resonance Width 495 10.9 Problems .................................496 Endnotes 501 11 Systems of Identical Particles 503 11.1 Indistinguishability ............................503 11.2 Second Quantization ...........................506 (a) Bose-Einstein Statistics 507 (b) Fermi-Dirac Statistics 513 (c) The Equations of Motion 516 (d) Distribution Functions 518 11.3 Ideal Gases ................................519 (a) The Grand Canonical Ensemble 520 (b) The Ideal Fermi Gas 521 (c) The Ideal Bose Gas 524 11.4 The Mean Field Approximation .....................526 (a) The Dilute Bose-Einstein Condensate 527 (b) The Hartree-Fock Equations 530 11.5 Problems .................................535 12 Interpretation 539 12.1 The Critique of Einstein, Podolsky and Rosen .............540 12.2 Hidden Variables .............................544 12.3 Bell s Theorem ..............................546 (a) The Spin Singlet State 547 (b) Bell s Theorem 548 (c) The Clauser-Horne Inequality 550 (d) An Experimental Test of Bell s Inequality 551 12.4 Locality ..................................554 12.5 Measurement ...............................558 (a) A Measurement Device 558 (b) Coherence and Entropy Following Measurement 568 (c) An Optical Analogue to the Stern-Gerlach Experiment 566 Contents xvii (d) A Delayed Choice Experiment 570 (e) Summation 572 12.6 Problems .................................574 Endnotes 575 13 Relativistic Quantum Mechanics 577 13.1 Introduction ................................577 13.2 The Dirac Equation ...........................579 (a) Lorentz Transformations of Spinors 580 (b) The Free-Particle Dirac Equation 58Ą (c) Charge and Current Densities 587 13.3 Electromagnetic Interaction of a Dirac Particle ............589 (a) The Dirac Equation in the Presence of a Field 589 (b) The Magnetic Moment 591 (c) The Fine Structure Hamiltonian 593 (d) Antiparticles and Charge Conjugation 595 13.4 Scattering of Ultra-Relativistic Electrons ................597 13.5 Bound States in a Coulomb Field ....................600 13.6 Problems .................................605 Endnotes 606 Appendix 607 Index 610
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spellingShingle	Gottfried, Kurt 1929-2022 Yan, Tung-Mow Quantum mechanics fundamentals Mecânica quântica larpcal Quantentheorie Quantum theory Yan, Tung-mow Quantenmechanik (DE-588)4047989-4 gnd
subject_GND	(DE-588)4047989-4
title	Quantum mechanics fundamentals
title_auth	Quantum mechanics fundamentals
title_exact_search	Quantum mechanics fundamentals
title_full	Quantum mechanics fundamentals Kurt Gottfried ; Tung-Mow Yan
title_fullStr	Quantum mechanics fundamentals Kurt Gottfried ; Tung-Mow Yan
title_full_unstemmed	Quantum mechanics fundamentals Kurt Gottfried ; Tung-Mow Yan
title_short	Quantum mechanics
title_sort	quantum mechanics fundamentals
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topic	Mecânica quântica larpcal Quantentheorie Quantum theory Yan, Tung-mow Quantenmechanik (DE-588)4047989-4 gnd
topic_facet	Mecânica quântica Quantentheorie Quantum theory Yan, Tung-mow Quantenmechanik
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