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Third edition

Cambridge : Cambridge University Press, 2021

xxi, 548 stran : ilustrace ; 26 cm

ISBN 978-1-108-47322-4 (vázáno)

Obsahuje bibliografii na stranách 541-543 a rejstřík

001636158

Preface page xiii // Preface to the Revised First Edition xvii // In Memoriam to J. J. Sakurai xix // Foreword from the First Edition xxi // 1 Fundamental Concepts // 1.1 The Stem-Gerlach Experiment 1 // 1.1.1 Description of the Experiment 2 // 1.1.2 Sequential Stem-Gerlach Experiments 4 // 1.1.3 Analogy with Polarization of Light 6 // 1.2 Kets, Bras, and Operators 10 // 1.2.1 Ket Space 10 // 1.2.2 Bra Space and Inner Products 12 // 1.2.3 Operators 13 // 1.2.4 Multiplication 14 // 1.2.5 The Associative Axiom 15 // 1.3 Base Kets and Matrix Representations 16 // 1.3.1 Eigenkets of an Observable 16 // 1.3.2 Eigenkets as Base Kets 17 // 1.3.3 Matrix Representations 18 // 1.3.4 Spin j Systems 21 // 1.4 Measurements, Observables, and the Uncertainty Relations 22 // 1.4.1 Measurements 22 // 1.4.2 Spin ~ Systems, Once Again 24 // 1.4.3 Compatible Observables 27 // 1.4.4 Incompatible Observables 29 // 1.4.5 The Uncertainty Relation 31 // 1.5 Change of Basis 33 // 1.5.1 Transformation Operator 33 // 1.5.2 Transformation Matrix 34 // 1.5.3 Diagonalization 35 // 1.5.4 Unitary Equivalent Observables 36 // 1.6 Position, Momentum, and Translation 37 // 1.6.1 Continuous Spectra 37 // 1.6.2 Position Eigenkets and Position Measurements 38 // 1.6.3 Translation 40 // 1.6.4 Momentum as a Generator of Translation 42 // 1.6.5 The Canonical Commutation Relations 45 // 1.7 Wave Functions in Position and Momentum Space 47 // 1.7.1 Position-Space Wave Function 47 // 1.7.2 Momentum Operator in the Position Basis 49 // 1.7.3 MomentunvSpace Wave Function 49 // 1.7.4 Gaussian Wave Packets 51 // 1.7.5 Generalization to Three Dimensions 53 // Problems 54 // 2 Quantum Dynamics 62 // 2.1 Time Evolution and the Schrödinger Equation 62 // 2.1.1 Time-Evolution Operator 62 // 2.1.2 The Schrödinger Equation 65 // 2.1.3 Energy Eigenkets 67 // 2.1.4 Time Dependence of Expectation Values 68 // 2.1.5 Spin Precession 69 //

2.1.6 Neutrino Oscillations 71 // 2.1.7 Correlation Amplitude and the Energy-Time Uncertainty Relation 74 // 2.2 The Schrödinger Versus the Heisenberg Picture 75 // 2.2.1 Unitary Operators 75 // 2.2.2 State Kets and Observables in the Schrödinger and the Heisenberg Pictures 77 // 2.2.3 The Heisenberg Equation of Motion 78 // 2.2.4 Free Particles: Ehrenfest’s Theorem 79 // 2.2.5 Base Kets and Transition Amplitudes 81 // 2.3 Simple Harmonic Oscillator 83 // 2.3.1 Energy Eigenkets and Energy Eigenvalues 83 // 2.3.2 Time Development of the Oscillator 88 // 2.4 Schrödinger’s Wave Equation 91 // 2.4.1 Time-Dependent Wave Equation 91 // 2.4.2 The Time-Independent Wave Equation 92 // 2.4.3 Interpretations of the Wave Function 94 // 2.4.4 The Classical Limit 96 // 2.5 Elementary Solutions to Schrödinger’s Wave Equation 97 // 2.5.1 Free Particle in Three Dimensions 97 // 2.5.2 The Simple Harmonic Oscillator 99 // 2.5.3 The Linear Potential 101 // 2.5.4 The WKB (Semiclassical) Approximation 104 // 2.6 Propagators and Feynman Path Integrals 108 // 2.6.1 Propagators in Wave Mechanics 108 // 2.6.2 Propagator as a Transition Amplitude 112 // 2.6.3 Path Integrals as the Sum over Paths 114 // 2.6.4 Feynman’s Formulation 115 // 2.7 Potentials and Gauge Transformations 120 // 2.7.1 Constant Potentials 120 // 2.1.2 Gravity in Quantum Mechanics 122 // 2.7.3 Gauge Transformations in Electromagnetism 126 // 2.7.4 The Aharonov-Bohm Effect 131 // 2.7.5 Magnetic Monopole 135 // Problems 138 // 3 Theory of Angular Momentum 149 // 3.1 Rotations and Angular Momentum Commutation Relations 149 // 3.1.1 Finite Versus Infinitesimal Rotations 149 // 3.1.2 Infinitesimal Rotations in Quantum Mechanics 152 // 3.1.3 Finite Rotations in Quantum Mechanics 153 // 3.1.4 Commutation Relations for Angular Momentum 154 // 3.2 Spin 1\2 Systems and Finite Rotations 155 // 3.2.1 Rotation Operator for Spin j 155 //

3.2.2 Spin Precession Revisited 157 // 3.2.3 Neutron Interferometry Experiment to Study 2n Rotations 158 // 3.2.4 Pauli Two-Component Formalism 159 // 3.2.5 Rotations in the Two-Component Formalism 161 // 3.3 SO(3), SU(2), and Euler Rotations 163 // 3.3.1 Orthogonal Group 163 // 3.3.2 Unitary Unimodular Group 164 // 3.3.3 Euler Rotations 166 // 3.4 Density Operators and Pure Versus Mixed Ensembles 169 // 3.4.1 Polarized Versus Unpolarized Beams 169 // 3.4.2 Ensemble Averages and Density Operator 170 // 3.4.3 Time Evolution of Ensembles 1*75 // 3.4.4 Continuum Generalizations 176 // 3.4.5 Quantum Statistical Mechanics 176 // 3.5 Eigenvalues and Eigenstates of Angular Momentum 18i1 // 3.5.1 Commutation Relations and the Ladder Operators 180 // 3.5.2 Eigenvalues of J2 and Jz 182 // 3.5.3 Matrix Elements of Angular-Momentum Operators 184 // 3.5.4 Representations of the Rotation Operator 185 // 3.6 Orbital Angular Momentum 188 // 3.6.1 Orbital Angular Momentum as Rotation Generator 188 // 3.6.2 Spherical Harmonics 191 // 3.6.3 Spherical Harmonics as Rotation Matrices 194 // 3.7 Schrodinger’s Equation for Central Potentials 195 // 3.7.1 The Radial Equation 196 // 3.7.2 The Free Particle and Infinite Spherical Well 198 // 3.7.3 The Isotropic Harmonic Oscillator 199 // 3.7.4 The Coulomb Potential 201 // 3.8 Addition of Angular Momenta 205 // 3.8.1 Simple Examples of Angular-Momentum Addition 205 // 3.8.2 Formal Theory o;’Angular-Momentum Addition 208 // 3.8.3 Recursion Relations for the Clebsch-Gordan Coefficients 212 // 3.8.4 Clebsch-Gordan Coefficients and Rotation Matrices 216 // 3.9 Schwinger’s Oscillator Model of Angular Momentum 218 // 3.9.1 Angular Momentum and Uncoupled Oscillators 218 // 3.9.2 Explicit Formula for Rotation Matrices 222 // 3.10 Spin Correlation Measurements and BelFs Inequality 224 // 3.10.1 Correlations in Spin-Singlet States 224 //

3.10.2 Einstein’s Locality Principle and Bell’s Inequality 226 // 3.10.3 Quantum Mechanics and Bell’s Inequality 229 // 3.11 Tensor Operators 231 // 3.11.1 Vector Operator 2 31 // 3.11.2 Cartesian Tensors Versus Irreducible Tensors 233 // 3.11.3 Product of Tensors 235 // 3.11.4 Matrix Elements of Tensor Operators; the Wigner-Eckart Theorem 236 // Problems 240 // 4 Symmetry in Quantum Mechanics 249 // 4.1 Symmetries, Conservation Laws, and Degeneracies 249 // 4.1.1 Symmetries in Classical Physics 249 // 4.1.2 Symmetry in Quantum Mechanics 250 // 4.1.3 Degeneracies 251 // 4.1.4 SO(4) Symmetry in the Coulomb Potential 252 // 4.2 Discrete Symmetries, Parity, or Space Inversion 256 // 4.2.1 Wave Functions under Parity 258 // 4.2.2 Symmetrical Double-Well Potential 261 // 4.2.3 Parity-Selection Rule 263 // 4.2.4 Parity Nonconservation 264 // 4.3 Lattice Translation as a Discrete Symmetry 265 // 4.4 The Time-Reversal Discrete Symmetry 270 // 4.4.1 Digression on Symmetry Operations 272 // 4.4.2 Time-Reversal Operator 275 // 4.4.3 Wave Function 279 // 4.4.4 Time Reversal for a Spin 1\2 System 280 // 4.4.5 Interactions with Electric and Magnetic Fields; Kramers // Degeneracy 283 // Problems 285 // 5 Approximation Methods 288 // 5.1 Time-Independent Perturbation heory: Nondegenerate Case 288 // 5.1.1 Statement of the Problem 288 // 5.1.2 The Two-State Problem 289 // 5.1.3 Formal Development of Perturbation Expansion 291 // 5.1.4 Wave Function Renormalization 295 // 5.1.5 Elementary Examples 296 // 5.2 Time-Independent Perturbation Theory: The Degenerate ase WO // 5.2.1 Linear Stark Effect 303 // 5.3 Hydrogenlike Atoms: Fine Structure and the Zeeman Elect 305 // 5.3.1 The Relativistic Correction to the Kinetic Energy 305 // 5.3.2 Spin-Orbit Interaction and line Structure 307 // 5.3.3 The Zeeman Effect 311 // 5.3.4 Van der Waals’ Interaction 314 // 5.4 Variational Methods 316 //

5.5 Time-Dependent Potentials: The Interaction Picture 320 // 5.5.1 Statement of the Problem 320 // 5.5.2 The Interaction Picture 321 // 5.5.3 Time-Dependent Two-State Problems: Nuclear Magnetic Resonance, Masers, and So Forth 323 // 5.5.4 Spin Magnetic Resonance 325 // 5.5.5 Maser 326 // 5.6 Flamiltonians with Extreme Time Dependence 327 // 5.6.1 Sudden Approximation 328 // 5.6.2 Adiabatic Approximation 328 // 5.6.3 Berry’s Phase 331 // 5.6.4 Example: Berry’s Phase for Spin \ 333 // 5.6.5 Aharonov-Bohm and Magnetic Monopoles Revisited 335 // 5.7 Time-Dependent Perturbation Theory 337 // 5.7.1 Dyson Series 337 // 5.7.2 Transition Probability 339 // 5.7.3 Constant Perturbation 341 // 5.7.4 Harmonic Perturbation 345 // 5.8 Applications to Interactions with the ( lassical Radiation Field 347 // 5.8.1 Absorption and Stimulated Emission 347 // 5.8.2 Electric Dipole Approximation 348 // 5.8.3 Photoelectric Effect 350 // 5.8.4 Spontaneous Emission 352 // 5.9 Energy Shift and Decay Width 355 // Problems 358 // 6 Scattering Theory 371 // 6.1 Scattering as a Time-Dependent Perturbation 371 // 6.1.1 Transition Rates and Cross Sections 373 // 6.1.2 Solving for the T Matrix 374 // 6.1.3 Scattering from the Future to the Past 376 // 6.2 The Scattering Amplitude 376 // 6.2.1 Wave Packet Description 381 // 6.2.2 The Optical Theorem 381 // 6.3 The Bom Approximation 384 // 6.3.1 The Higher-Order Bom Approximation 387 // 6.4 Phase Shifts and Partial Waves 388 // 6.4.1 Free-Particle States 388 // 6.4.2 Partial-Wave Expansion 392 // 6.4.3 Unitarity and Phase Shifts 394 // 6.4.4 Determination of Phase Shifts 397 // 6.4.5 Hard-Sphere Scattering 398 // 6.5 Eikonal Approximation 400 // 6.5.1 Partial Waves and the Eikonal Approximation 403 // 6.6 Low-Energy Scattering and Bound States 405 // 6.6.1 Rectangular Well or Barrier 406 // 6.6.2 Zero-Energy Scattering and Bound States 408 //

6.6.3 Bound States as Poles of Si(k) 410 // 6.7 Resonance Scattering 412 // 6.8 Symmetry Considerations in Scattering 416 // 6.9 Inelastic Electron-Atom Scattering 419 // 6.9.1 Nuclear Form Factor 423 // Problems 424 // 7 Identical Particles 429 // 7.1 Permutation Symmetry 429 // 7.2 Symmetrization Postulate 433 // 7.3 Two-Electron System 434 // 7.4 The Helium Atom 437 // 7.5 Multiparticle States 441 // 7.6 Density Functional Theory 443 // 7.6.1 The Energy Functional for a Single Particle 443 // 7.6.2 The Hohenberg-Kohn Theorem 445 // 7.6.3 The Kohn-Sham Equations 447 // 7.6.4 Models of the Exchange-Correlation Energy 450 // 7.6.5 Application to the Helium Atom 451 // 1.1 Quantum Fields 454 // 7.7.1 Second Quantization 454 // 7.7.2 Dynamical Variables in Second Quantization 456 // 7.7.3 Example: The Degenerate Electron Gas 460 // 7.8 Quantization of the Electromagnetic Field 464 // 7.8.1 Maxwell’s Equations in Free Space 465 // 7.8.2 Photons and Energy Quantization 467 // 7.8.3 The Casimir Effect 468 // 7.8.4 Concluding Remarks 472 // Problems 474 // 8 Relativistic Quantum Mechanics 478 // 8.1 Paths to Relativistic Quantum Mechanics 478 // 8.1.1 Natural Units 479 // 8.1.2 The Energy of a Free Relativistic Particle 479 // 8.1.3 The Klein-Gordon Equation 480 // 8.1.4 An Interpretation of Negative Energies 484 // 8.1.5 The Klein-Gordon Field 485 // 8.1.6 Summary: The Klein-Gordon Equation and the Scalar Field 489 // 8.2 The Dirac Equation 490 // 8.2.1 The Conserved Current 491 // 8.2.2 Free-Particle Solutions 493 // 8.2.3 Interpretation of Negative Energies 494 // 8.2.4 Electromagnetic Interactions 495 // 8.3 Symmetries of the Dirac Equation 496 // 8.3.1 Angular Momentum 497 // 8.3.2 Parity 497 // 8.3.3 Charge Conjugation 498 // 8.3.4 Time Reversal 499 // 8.3.5 CPT 501 // 8.4 Solving with a Central Potential 502 // 8.4.1 The One-Electron Atom 505 // 8.5 Relativistic Quantum Field Theory 509 //

Problems 510 // Appendix A Electromagnetic Units 514 // Appendix B Elementary Solutions to Schrodinger’s Wave Equation 520 // Appendix C Hamiltonian for a Charge in an Electromagnetic Field 530 // Appendix D Proof of the Angular-Momentum Rule (3.358) 532 // Appendix E Finding Clebsch-Gordan Coefficients 534 // Appendix F Notes on Complex Variables 535 // Bibliography 541 // Index 544