Physics 412-2
Quantum Mechanics II
Winter 2021
J. A. Sauls

Lectures: January 11 - March 11
When: Monday, Wednesday & Friday 10:00 - 11:00
Where: Zoom via Canvas

This is the second of a three-quarter sequence of a graduate-level course on quantum mechanics and its applications to the microphysical world. I expand on the foundations of quantum mechanics, wave mechanics, the impact of symmetries on quantum state dynamics, with applications in atomic, molecular and nuclear physics, with methods of approximation and perturbation theory along the way.

References:
  1. Principles of Quantum Mechanics, R. Shankar, Springer (1994)
  2. Sakurai I: Modern Quantum Mechanics, J. J. Sakurai, Addison-Wesley (1993)
  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.

Course Evaluation: Graded Problem Sets [25%], Mid-Term Exam [25%], Final Exam [50%]

Syllabus

  1. Feynman's Formulation of QM
    1. Amplitudes as a Sum over Paths
    2. Principle of Least Action
    3. Feynman's Propagator
    4. Schrödinger's Wave Equation
    5. Aharonov-Bohm Effects
    6. Berry Phase
  2. Quantum Mechanics of Charged Particles
    1. Electromagnetic Potentials
    2. Aharonov-Bohm Effects
    3. Electron in a Uniform Magnetic Field
    4. Rydberg Atoms: Electron in a Coulomb Field
    5. Fine Structure
    6. Electron Spin: Pauli's Theory
    7. Zeeman & Stark effects
  3. Symmetry in Quantum Mechanics II
    1. Representations of the Rotation group
    2. Half-Odd Integer Representations: Spin 1/2
    3. Tensor Operators: Wigner-Eckhardt theorem
    4. Discrete Symmetries: P,T
    5. Indistinguishability: Permutation Symmetry
  4. Approximation Methods
    1. Dimensional Analysis
    2. Bound state Perturbation theory
    3. Degenerate Perturbation theory
    4. Variational Principles
    5. Semi-classical Approximation
  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 Approximation
    5. H2, H2: Heitler-London approximation
    6. Molecular Vibrations & Rotations
  4. Time-dependent Perturbations
    1. Transition Rate - Fermi's Golden Rule
    2. Electric Dipole Radiation of Atoms
    3. Nuclear Magnetic Resonance
    4. Nearly Adiabatic Dynamics


File translated from TEX by T TH, version 3.81.
On 1 December 28, 2020.