Physics 412-3
Quantum Mechanics III
Spring 2022
J. A. Sauls

Lectures: March 29 - June 4
When: Monday, Wednesday & Friday 10:00 - 11:00
Where: Tech Room M152

This is the third of a three-quarter sequence of a graduate-level course on quantum mechanics and its applications to the microphysical world. This quarter expands the foundations of quantum mechanics to many particle systems, with applications to atomic and molecular structure, radiative transitions in atoms. The theory of identical particles in quantum mechanics stretches over some of the most peculiar and important predictions of quantum mechanics, from the Casimir force between metal surfaces, vacuum fluctuations, spontaneous emission of photons, to entagled quantum states.

Syllabus

  1. Atomic Structure
    1. Rydberg Atoms: Electron in a Coulomb Field
    2. Zeeman & Stark effects
    3. Electron Spin: Pauli's Theory
    4. Spin-Orbit Interaction & Fine Structure
    5. Hyperfine Structure
  2. Relativistic Wave Mechanics
    1. Klein-Gordon Equation
    2. Dirac's theory
    3. Electron Spin
    4. Fine structure of H
    5. Hole theory - positrons
  3. Identical particles
    1. Indistinguishability in Quantum Mechanics
    2. Permutation Exchange Symmetry
    3. Statistical Correlations: Fermions & Bosons
    4. Bose and Fermi Gases
    5. Bose-Einstein Condensation
    6. Free Fermions - Fermi Sea
    7. Second Quantization: Fock space
  4. Multi-electron Atoms
    1. Many-electron Atoms: Helium
    2. Thomas-Fermi model
    3. Hartree-Fock theory
    4. Electron Correlations: H
    5. Atomic structure, Hund's rules
  5. Quantum Mechanics of the EM Field
    1. Quantization of the Radiation Field
    2. Fock States for Photons
    3. Momentum & Angular Momentum
    4. Number-Phase Uncertainty
    5. Coherent States of Radiation
    6. Fluctuations of the Radiation Field
    7. Vacuum Fluctuations & the Casimir Effect
  1. Time-dependent Perturbations
    1. Transition Rate - Fermi's Golden Rule
    2. Electric Dipole Radiation of Atoms
    3. Nuclear Magnetic Resonance
    4. Nearly Adiabatic Dynamics
  2. Interaction of Radiation & Matter
    1. Radiative Transitions of Atoms
    2. Multipole transitions
    3. Spontaneous emission
    4. Photoelectric Effect
    5. Nonresonant Optical Response
    6. Optical Birefringence
    7. Thomson scattering
    8. Rayleigh scattering
    9. Raman scattering
    10. Lamb Shift of Hydrogen
  3. Scattering Theory
    1. Potential Scattering
    2. Scattering of Wave packets
    3. Steady-State Theory
    4. Lipmann-Schwinger Equation
    5. Born Approximation
    6. Cross-Sections, Optical Theorem
    7. Scattering Resonances
  4. Quantum Optics
    1. Photon Statistics and Correlations
    2. Quantum Coherence & Measurment Theory
    3. Squeezed states & the Uncertainty Principle
    4. Stimulated Emission & LASER
  5. Macroscopic Quantum Mechanics
    1. Bose-Einstein Condensation
    2. Gross-Pitaevskii Theory
    3. Topology and Quantum Theory
    4. Macroscopic Phase Coherence
References:
  1. Principles of Quantum Mechanics, 2nd Edition, R. Shankar, Plenum Press (1994)
  2. Principles of Quantum Mechanics, 4th ed., P.A.M. Dirac, Oxford Press (1958).
  3. Lectures on Quantum Mechanics, S. Weinberg, Cambridge University Press (2012)
  4. Lectures on Quantum Mechanics, G. Baym, Benjamin/Cummings Pub. Co. (1969).
  5. Quantum Mechanics, Vol. 3, L. Landau & I. Lifshitz, Pergamon Press (1977).
  6. Intermediate Quantum Mechanics, 3rd ed., H. Bethe and R. Jackiw (1986).
  7. Sakurai II: Advanced Quantum Mechanics, J. J. Sakurai, Addison-Wesley (1967)
  8. Handbook of Mathematical Functions, M. Abramowitz & A. Stegun, National Bureau of Standards, Washington DC (1952). Online Version maintained by Collin MacDonald.

    File translated from TEX by T TH, version 3.81.
    On March 3, 2022.