Physics 412-3
Quantum Mechanics III
Spring 2021
J. A. Sauls

Lectures: March 30 - June 4
When: Monday, Wednesday & Friday 10:00 - 11:00
Where: Lecture Room 4 & Zoom via Canvas

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 potentially important predictions of quantum mechanics, from the Casimir's force between metal surfaces to entagled states of identical particles.
Course Evaluation: Graded Problem Sets [25%], Mid-Term Exam [25%], Final Exam [50%]

Syllabus

  1. Relativistic Wave Mechanics
    1. Klein-Gordon Equation
    2. Dirac's theory
    3. Electron Spin
    4. Fine structure of H
    5. Hole theory - positrons
  2. Identical particles in Quantum Theory
    1. Indistinguishability in Quantum Mechanics
    2. Permutation Exchange Symmetry
    3. Second Quantization: Fock space
    4. Statistical Correlations: Fermions & Bosons
    5. Fractional Statistics in 2D
  3. Atoms & Molecules
    1. Two-electron Atoms
    2. Many-electron Atoms
    3. Atomic structure, Hund's rules
    4. Molecules: Born-Oppenheimer Theory
    5. H2, H2: Heitler-London approximation
    6. Molecular Vibrations & Rotations
  4. 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. Photon Statistics
    7. Fluctuations of the Radiation Field
    8. Vacuum Fluctuations & the Casimir Effect
  1. Quantum Optics
    1. Photon Statistics and Correlations
    2. Squeezed states & the Uncertainty Principle
    3. Stimulated Emission & the theory of LASER
    4. Quantum Coherence & Measurment Theory
  2. Time-dependent Perturbations
    1. Transition Rate - Fermi's Golden Rule
    2. Electric Dipole Radiation of Atoms
    3. Nuclear Magnetic Resonance
    4. Nearly Adiabatic Dynamics
  3. Interaction of Radiation & Matter
    1. Radiative Transitions of Atoms
    2. Multipole transitions
    3. Spontaneous emission
    4. Photoelectric Effect
    5. Nonresonant Optical Response
    6. Inelastic light scattering
    7. Lamb Shift of Hydrogen
  4. Scattering Theory
    1. Potential Scattering
    2. Scattering of Wave packets
    3. Lipmann-Schwinger Equation
    4. Cross-Sections, Optical Theorem
    5. Scattering Resonances
    6. Inelastic scattering & Molecular Excitations
    7. Correlation Functions & Structure Factors

References:
  1. Principles of Quantum Mechanics, R. Shankar, Springer (1994)
  2. Sakurai II: Advanced Quantum Mechanics, J. J. Sakurai, Addison-Wesley (1967)
  3. Lectures on Quantum Mechanics, G. Baym, Benjamin/Cummings Pub. Co. (1969).
  4. Quantum Mechanics, 3rd ed., Vol. 3, L. Landau & I. Lifshitz, Pergamon Press (1977).
  5. The Principles of Quantum Mechanics, 4th ed., P. A. M. Dirac, Oxford Press (1958).
  6. Intermediate Quantum Mechanics, 3rd ed., H. Bethe and R. Jackiw (1986).
  7. Lectures on Quantum Mechanics, S. Weinberg, Cambridge University Press (2012)
  8. Handbook of Mathematical Functions, M. Abramowitz and 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 30, 2021.