PHYSICS 64-544 Theory of Atomic Structure and Atomic Spectra

Lectures so far:

 May 17 1/2 hour Introduction, exact diagonalization vs. pert.
 theory
 Assignment:
  - prove that a power series expansion for the exact diagonalization
     of a 2 x 2 matrix is the same as perturbation theory up to
     second order.

 May 19 1 hour: Schrodinger equation, Z-scaling, units
 Assignment:
   - Derive the Z-scaled Schrodinger equation.

 May 31 no lecture (all research)

 June 2 Hartree-Fock and configuration interaction (C.I.)
 Assignment:
   - derive the H.F. equations
   - prove that the variational principle is equivalent to
   diagonalization of the Hamiltonian.

 June 7 1/2 hour - completeness & Sturmian functions
 Assignment:
   - Derive the orthogonality condition for Sturmian functions.
   - Find and read Ince's book on Sturmian functions.
   - show that the r.h.s of the spherical harmonic addition theorem
     for cos(theta12) is rotationally invariant.

 June 9 1 hour - brute force method and the power method for the
   generalized eigenvalue problem.
 Assignment
   - Write a program to solve the generalized eigenvalue problem
   for hydrogen s-states, assuming basis functions of the form
   phi_i = r^i exp(-alpha r)

 June 21 1/2 hour - discussion of matrix diagonalization by Jacobi's
   method, and formalism to write all N eigenvectors simultaneously
   as a matrix.

June 28 1 hour - discuss sample program hbasis4.for, Jacobi method
and power method.
   - review spherical harmonics
   - derive expression for del^2 in Hylleraas coords.

July 5 1 hour - angular integrals and radial recursion relations.

 July 12
          July 14  no lecture - in Montreal
 July 19  Hermitian form for the Hamiltonian
 July 21  small corrections - finite nuclear mass

 Aug. 2 Begin angular momentum algebra pp 1-5.
 Aug. 4 pp. 6-10.


 Future Topics

 1.  remainder of notes on solving the Schroedinger equation for
 helium.
 2.  Dirac equation and relativistic effects in atomic physics.
 3.  introduction to quantum electrodynamics (QED).
 4.  introduction to group theory and symmetry operations.
 5.  angular momentum coupling.
 6.  Wigner-Eckart theorem.
 7.  3-j and 6-j symbols.
 8.  diagrammatic techniques for angular momentum coupling.