Part 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, Schedule, PHYS424 home

PHYS 424 Notes

Outline

  1. Chapter 1.
    1. Administrative Matters
    2. Double slit
      1. Waves and double slits
    3. Double Slit [continued]
      1. Low Intensity
        1. Experimental result
        2. Interpretation
    4. Probability
      1. Discrete possibilities
      2. Continuous possibilities
      3. Some subtleties
    5. Statistical Interpretation of the Wave Function
    6. Schroedinger Equation
    7. Normalization
    8. Uncertainty Principle
  2. Chapter 2.
    1. Overview
    2. Stationary States
    3. Infinite Square Well
    4. Harmonic Oscillator
    5. Delta Functions
    6. Free Particle
      1. Schroedinger Equation and solution
      2. Wave packets
    7. Finite Square Well
      1. General Information
      2. E<0
      3. E>0
  3. Chapter 3.
    1. Linear Algebra
      1. Vectors
      2. Inner Products
      3. Linear Transformations
        1. Symmetric Matrices
        2. Antisymmetric Matrices
        3. Hermitian Matrices
        4. [Skew Hermitian Matrices]
        5. Inverses
      4. Change of basis
      5. Hermitian Transformations and Operators
      6. Eigenvectors and Eigenvalues
    2. Function Spaces
      1. Functions as vectors
      2. Operators as linear transformations
      3. Hilbert space
    3. Statistical Interpretation
      1. States are vectors
      2. Observables are eigenvalues of Hermitian operators
      3. Momentum space
    4. Uncertainty Principle
      1. Proof
      2. The minimum-uncertainty packet
      3. DEDt
  4. Chapter 4.
    1. Spherical Coordinates
      1. Generalization to three dimensions
      2. Separation of variables
      3. Angular equation
        1. Legendre polynomials
        2. Associated Legendre polynomials
        3. Spherical harmonics
      4. Spherical Well
        1. Energies
        2. Spherical Bessel functions
      5. Hydrogen Atom
        1. Potential energy
        2. Solution of the radial equation
          1. Energies
          2. Associated Laguerre polynomials
          3. Hydrogen spectrum
      6. (Harmonic Oscillator)
    2. Angular Momentum
      1. Operators
      2. Commutators
      3. Algebraic determination of eigenvalues
      4. Eigenfunctions
    3. Spin
      1. Spin 1/2
      2. Electron in a magnetic field
    4. Addition of angular momenta
  5. Chapter 5.
    1. Two-Particle Systems
    2. Atoms
  6. Chapter 6.
    1. Nondegenerate Perturbation Theory
    2. Degenerate Perturbation Theory
    3. Fine Structure of Hydrogen
    4. Zeeman Effect
    5. Hyperfine Splitting
Last Revised 02/09/13