LECTURES ON QUANTUM MECHANICS
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1 LECTURES ON QUANTUM MECHANICS GORDON BAYM Unitsersity of Illinois A II I' Advanced Bock Progrant A Member of the Perseus Books Group
2 CONTENTS Preface v Chapter 1 Photon Polarization 1 Transformation of Bases 8 Angular Momenhun 13 Amplitude Mechanics 20 Unpolarized Light 25 Behavior of Photon Polarization in Matter Chapter 2 Neutral K Mesons 38 Quantum Interference Effects Chapter 3 The Motion of Particles in Quantum Mechanics 46 The Schrödinger Equation 46 State Vectors 53 Digression an the Delta Function 55 Operators for Physical Quantities 59 The Free Particle 62 Quantum Mechanical Motion as a Sum over Paths 69 Particle in a Magnetic Field 74 Aharonov-Bohm Effect Chapter 4 Potential, Mostly in One Dimension 83 Properties of Hermitian Operators 83 vii
3 viii CONTENTS Energy Eigenstates 85 One-Dimensional Barriers 88 Tunneling 93 Bound States 97 Parity 99 Transmission Resonances 104 One-Dimensional Delta Function Potential 113 Periodic Potentials 116 The Harmonic Oscillator Chapter 5 Equations of Motion for Operators 134 Functions of Operators 134 Heisenberg Representation 136 Formal Solution for the Time Development Operator Chapter 6 Orbital Angular Momentum and Central Potentials 148 Commutation Relations 148 Rotation 150 Differential Operator Representation 153 Eigenfunctions and Eigenvalues 155 Spherical Harmonics 159 Central Forces Chapter 7 The Hydrogen Atom Two Particle Systems Hydrogen Atom Wave Functions The Symmetry of the Hydrogen Atom Chapter 8 Cooper Pairs Chapter 9 Potential Scattering Wave Packets Cross Sections Partial Waves The Optical Theorem The Born Approximation Properties of the Scattering Amplitude
4 CONTENTS Low Energy Resonances ix Chapter 10 Coulomb Scattering 213 Analytic Properties of the Scattering Amplitude 217 Regge Poles Chapter 11 Stationary State Perturbation Theory 225 The Wave Function Renormalization Constant 229 Degenerate Perturbation Theory 231 Van der Waals Interaction 234 Almost Degenerate Perturbation Theory 237 Brillouin Wigner Perturbation Theory 241 Nonperturbative Methods Chapter 12 Time-Dependent Perturbation Theory 246 First-Order Transitions: Golden Rule 248 Harmonic Perturbations 255 Second-Order Transitions 257 Forward "Scattering»Amplitude Chapter 13 Interaction of Radiation with Matter 262 Interaction Hamiltonian 264 Absorption of Light 267 Quantized Radiation Field 271 Einstein's A and B Coefficients 276 Details of Spontaneous Emission 278 Electric Dipole Transitions 281 Magnetic Dipole and Electric Quadrupole Transitions 287 Scattering of Light 289 Raman Scattering Chapter 14 Spin 1/2 302 Rotations in Spin Space 305 Including Spatial Degrees of Freedom 308 Spin Magnetic Moment 310 Precession 315 Spin Resonance 317
5 x CONTENTS Motion in Inhomogeneous Magnetic Fields Chapter 15 Addition of Angular Momenta 332 Addition of Two Angular Momenta 335 Clebsch Cordan Technology 338 Scattering of Spin 1/2 Particles with Spinless Particles 342 Three Angular Momenta Chapter 16 Isotopic Spin Chapter 17 Rotations and Tensor Operators 358 Representations of Rotations 358 Tensor Operators 367 Multipole Radiation 376 Angular Momentum and the Harmonie Oscillator Chapter 18 Identical Particles Permutation and Symmetry States of Noninteracting Identical Particles Scattering of Identical Particles Identity and Isotopic Spin Chapter 19 Second Quantization Creation and Annihilation Operators Second Quantized Operators Pair Correlation Functions The Hanbury Brown and Twiss Experiment The Hamiltonian Chapter 20 Atoms Two-Electron Atoms Hartree Approximation Fermi Thomas Approximation Hartree Fock The Periodic Table Splitting of Configurations
6 CONTENTS xi Spin-Orbit Interaction 460 Spin-Orbit Splitting in Hartree-Fock 462 Zeeman Effect Chapter 21 Molecules 469 Born-Oppenheimer Method 471 The 112 Ion The Hydrogen Molecule 479 Pairing of Electrons 483 Spatially Directed Orbitals 486 Hybridization 489 Hydrocarbons 495 Chapter 22 Relativistic Spin Zero Particles: Klein-Gordon Equation 499 Negative Energy States and Antiparticles 504 First-Order Klein--Cordon Equation 507 Free Particle Wave Packets 513 Klein's Paradox 515 Scattering by a Potential 520 Bound State 524 Nonrelativistic Limit 529 Scalar Interactions 531 Neutral Particles Chapter 23 Relativistic Spin 1/2 Particles: Dirac Equation 534 Lorentz Transformation of Spin 534 Dirac Equation 543 Free Particle Solutions 548 Currents 552 Nonrelativistic Limit 558 Second-Order Dirac Equation 563 Dirac Hydrogen Atom 564 Hyperfine Structure 572 The Lamb Shift 574 Dirac Hole Theory Index 589
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