PHY 212: Lecture Highlights.

14 Jan 2010:

• Motivation for perturbation theory: corrections to gross H atom
• Example of relativistic energy-momentum relationship expanded for low velocities
• Perturbation theory is valid if size of correction is "small" compared to unperturbed energies
• Be able to derive expressions for perturbative corrections to energy eigenvalues and their associated eigenvectors.

19 Jan 2010:

• Example of anharmonic oscillator
• Hint: review raising and lowering operators for SHO

21 Jan 2010:

• Variational method: general variational parameters
• Be able to prove the minimization limit
• Example: trial function for SHO

26 Jan 2010:

• Linear variational method
• Truncation of basis state space
• Relationship to perturbation theory
• Application to degenerate subspace

28 Jan 2010:

• The Stark Effect -- ground state (quadratic)
• The Stark Effect -- first excited state; deg. pert. thy.
• Motivation for selection rules
• Angular momentum spectrum from commutation relations

2 Feb 2010:

• Addition of angular momentum
• Clebsh-Gordan coefficients
• Example in H atom.

4 Feb 2010:

• Rotations
• Finding minimum and maximum total j values
• (l=1) x (s=1/2) = (j=3/2) + (j=1/2) example

9 Feb 2010:

• Wigner-Eckart theorem

11 Feb 2010:

• Review for Exam 1
• Wigner-Eckart, continued
• Classical analogue: projection theorem

16 Feb 2010:

• Fine structure for H atom: applying W-E

18 Feb 2010:

• Take Exam 1

23 Feb 2010:

• EM transitions between H atom energy levels
• Spin-orbit term
• Darwin term
• Collecting the fine structure corrections

25 Feb 2010:

• Exam 1 discussion
• Including a B field: Zeeman effect vs spin-orbit term

2 Mar 2010:

• Weak/strong magnetic field limit vs fine structure
• Hyperfine structure and external magnetic fields

4 Mar 2010:

• Time-dependent perturbation theory
• Example of time-dependent electric field induced 2s -> 2p transition

16 Mar 2010:

• Einstein Coefficients

18 Mar 2010:

• Calculation of lifetime again spontaneous decay
• Degeneracies and line strength
• Magnetic dipole and electric quadrupole terms

23 Mar 2010:

• Fermi's Golden Rule
• Identical particles; symmetrization operators
• Single particle orbitals

25 Mar 2010:

• Review for Exam II
• Perturbation theory for identical particle systems

30 Mar 2010:

• Exam II

1 Apr 2010:

• He atom
• Direct and exchange integrals
• Slater determinants

6 Apr 2010:

• Residual and spin-orbit effects
• Allowed spectrascopic terms and sublevels

8 Apr 2010:

• LS coupling energy shifts
• Selection rules; matching spectra to available transitions

13 Apr 2010:

• Scattering. Definition of differential cross section
• Born approximation. Yukawa example

15 Apr 2010:

• Partial wave expansion.
• Hard sphere example

20 Apr 2010:

• WKB approximation

22 Apr 2010:

• Bound state example
• Introduction to path integrals
• Central field approximation

27 Apr 2010:

• Go over exam II
• Review for final
• Evaluations