Lecture Topics for PHYS 475
  1. Jan. 4, 2011
    1. Discussion of Course Outline
    2. Evidence for Atoms (conjecture by Greeks, kinetic molecular theory, Brownian motion, direct observation)
    3. Electrons as a fundamental part of atomic structure (electrolysis)
    4. Electromagnetic nature of atomic structure
  2. Jan. 5, 2011
    1. Further early atomic investigations
      1. Thomson's e/m, cathode ray experiments
      2. Millikan oil drop to measure quantized charges
      3. Rutherford's evidence for a nuclear atom
      4. Failure of a classical atomic model
    2. Spectroscopic observations (classroom demonstration)
      1. Distinct emission lines of electrical discharge through atomic gases
      2. Uniqueness of lines
      3. Colour/Energy Bands in molecular gases
      4. Fluorescent lights: bands with lines
      5. Incandescence: black body spectrum
      6. Absorption lines in the solar spectrum
    3. Explanations of spectral lines
      1. Rydberg-Ritz formula for hydrogen and one-electron atoms
      2. Wavenumber and the Ritz combination principle
      3.  Classical EM: oscillating electrons like musical notes?
      4. Difficulties measuring IR and UV lines
  3. Jan. 7
    1. The Bohr Model
      1. Quantized photons
      2. Circular orbits and planetary model
      3. Quantised angular momentum
      4. Quantised radii and energy
      5. Common units
      6. Explanation of the Rydberg-Ritz formula
    2. Isotope shift and higher Z single-electron atoms/ions
  4. Jan. 11
    1. Relativistic corrections to the Bohr model
      1. Suggestion by Sommerfeld that ellipitical orbits with identical L and gross E are possible
      2. Relativistic corrections are related to (v/c)2
      3. Percentage energy shift related to (a/n)2
      4. For hydrogen fine structure of 1 cm-1
    2. Moseley's measurement of characteristic X-rays
      1. Square-root of frequency related to atomic number; first measurement of Z
      2. Can explain roughly linear behaviour by using shell-Bohr model with shielding factors
      3. Convenience of thinking of holes dropping from K-shell to L and M shells
      4. Increase of fine structure energies for higher Z
  5. Jan. 12
    1. Radiative decay
      1. Use of classical electric dipole radiation formula
      2. Decay times that are several million times the period of oscillation
      3. Gives good estimates if the transition is not-disallowed by selection rules (we'll see those later)
    2. Einstein coefficients
      1. Two-level atom with degeneracy interacting with radiation
      2. A rate equation involving absorption, stimulated emission, and spontaneous emission.
      3. Using thermal equilibrium and Boltzmann statistics to establish relations between A and B coefficients
  6. Jan. 14
    1. Zeeman effect
      1. Relative scale 10 GHz or 1 part in 5000
      2. A classical 3-D harmonic oscillator with a Lorentz force perturbation
      3. The Larmor frequency WL
      4. Larmor frequency gives matrix-cross terms which give new, shifted eigenfrequencies
      5. Oscillation along z-axis is unaffected; the p-line
  7. Jan. 18
    1. Zeeman effect cont'd
      1. New circular eigenmodes with shifted frequences the s+ and s- lines
      2. Polarizations when viewing transverse and longitudinally to the magnetic field
    2. Chapter 2: Quantum mechanical treatment of H-atom
      1. Using spatial rep for Hamiltonian
      2. Relative coordinates and reduced masses implied
  8. Jan. 19
    1. Quantum mechanical treatment of H-atom cont'd
      1. Separation of r and angular coordinates in the Laplacian and in y
      2. Angular momentum in the Laplacian
      3. Separation of q and f coordinates
      4. Eigenfunctions and eigenvalues of F(f)
      5. Using ladder operators to generate new Yb
      6. Commutators of ladder operators
  9. Jan. 21
    1. The Ylm functions
      1. Finding the form for the m=mmax=l Y-function
      2. Establishing the value for b
      3. Generating the Ylm functions
      4. Cartesian forms of Ylm
      5. Angular distributions
  10. Jan. 25
    1. Solving the radial equation
      1. Transforming to P=rR function
      2. Looking at P as the solution to 1-D Schrodinger equation
      3. Transforming to dimensionless distance r and potential energy l
      4. Quantisation/eigenvalue condition imposed on l
      5. The quantum mechanical derivation of the Bohr formula
      6. Some expectation values and wavefunctions
  11. Jan. 26
    1. Transitions between states in H
    2. Elements of time-dependent perturbation theory: Fermi's Golden Rule
    3. The electric dipole approximation for the electromagnetic field
    4. The perturbing Hamiltonian
    5. Splitting of the matrix element into radial and angular integrals
  12. Jan. 28
    1. What does ȓ do as an operator?  Answer: creates more spherical harmonics
    2. Using a basis set of "spherical" vectors since they have simple operation properties
    3. Selection rule Dm=0 for Ap type radiation
  13. Feb. 2
    1. Summary of m selection rules
    2. Dl=±1
      1. Argument based on spherical harmonic identity
      2. Argument based on parity operator
    3. Relativistic corrections
      1. Electron spin/ spin operator algebra
  14. Feb. 4
    1. Origin of spin-orbit interaction
    2. The Bohr magneton
    3. Using conventional operators to describe the perturbing Hamiltonian
    4. Expression for the spin-orbit energy shift
    5. Trying to find eigenstates of j in order to determine s·l
  15. Feb. 8
    1. Slight review of the spin-orbit splitting, similarity to earlier estimates
    2. Using the old eigenstates to construct new eigenstates that are eigenstates of new Hamiltonian but not lz and sz
    3. Clebsch-Gordan coefficents
    4. Labelling states with the LS coupling scheme
    5. Degeneracy of 2s 2S1/2 and 2p 2P1/2 even after relativistic corrections
  16. Feb. 11
    1. Lamb shift
      1. Difficultly of resolving fine structure of Ha line because of Doppler broadening
      2. Lamb-Retherford experiment in 1947
      3. Metastable 2s 2S1/2 state
      4. RF cavity and Zeeman shift
      5. Quantum electrodynamics to calculate 2s 2S1/2 and 2p 2P1/2 1059 MHz splitting
  17. Feb. 15
    1. Helium
      1. Non-interacting ground state
      2. Calculation of repulusion perturbation for ground state
      3. Variational approach gives slightly better results
    2. Excited states of helium
  18. Feb. 16
    1. Degenerate pertubation theory
    2. J-K matrix and solving for eigenvalues and eigenvectors
    3. Direct and exchange energies
  19. Feb. 18
    1. n.b. the linear combinations are eigenstates to 1st order only
    2. Behaviour of J and K if we separate out 1/r12
    3. Spin states associated with ySspace and yAspace
    4. "Spin Dependent" splitting of 1L and 3L states
    5. Convergence to hydrogen energy levels
  20. March 1
    1. Labelling of energy levels
    2. Assigning spectral lines to transitions
    3. Possibility of using new 'J'
    4. Ground state J integral 34 eV using "enclosed charge" method
  21. March 2
    1. J and K integrals for excited states
      1. Separation into spatial and angular parts
      2. Expressing 1/r12 in terms of spherical harmonics
  22. March 4
    1. Brief review of some concepts from Chapter 3
    2. Chapter 4: Alkalis
      1. Shell structure
      2. Using Bohr model for excited states
      3. The "ell" dependent quantum defect
  23. March 15
    1. Using a central potential to account for electrostatic repulsion
      1. Separation of equation
      2. Transformation to radial equation
      3. Numerical solution of radial equation
  24. March 16
    1. Slater determinant
    2. A more QM approach to J=L+S
    3. Fine structure in alkalis and the Lande formula
    4. Relationship of spin-orbit coupling to 1/r3 expectation value
  25. March 18
    1. Scaling in the Lande formula
    2. Relative intensities from fine-structure splitting
    3. Numerical solution to Schrodingers radial equation (Exercise 4.10)
  26. March 22
    1. Using Matlab to work through 4.10
      1. Energy resolution
      2. Using nodes to label the levels
      3. Modification to Zeff
      4. Difference for different ell values
      5. Using solutions to find new potentials
  27. March 23
    1. Russell-Saunders or LS coupling scheme
      1. Residual electrostatic interaction to account for exchange
      2. Total L and total S as good quantum numbers
      3. Terms
      4. Equivalent electrons and Hund's rules
  28. March 25
    1. Fine-structure in LS coupling and projection rule
    2. Interval rule for fine-structure
    3. Possibility of a jj  coupling for heavy atoms
  29. March 29
    1. Configurations, terms, levels, and states
    2. Selection rules for LS coupling scheme
      1. Violation for jj coupling scheme: intercombination lines in large Z  systems
    3. Zeeman effect
      1. Lande g-factor
      2. Multiple lines for anomalous Zeeman effect
  30. April 1
    1. Hyperfine structure
      1. Fermi contact interaction
      2. IJ coupling to give F
      3. Hyperfine splitting of hydrogen 1.42 GHz
      4. Hydrogen maser
  31. April 1
    1. Extension to ell not equal to 0 states
    2. Z dependence of HFS
    3. Interval rule for HFS and assigning quantum numbers
    4. Isotope shift
    5. Volume effect
  32. April 5
    1. HFS and the Zeeman effect
      1. Weak field with IJ coupling
      2. Strong field when J precesses around B
      3. Intermediate field region with no crossing
  33. April 6
    1. Measuring hyperfine structure
      1. Fabry-Perot when HFS exceeds Doppler effect
      2. Doppler-free laser spectroscopy
      3. NMR, chemical shift
      4. Atomic beam (double Stern-Gerlach) technique
    2. Atomic clocks based on hyperfine structure