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.
Aug. 8 pp. 11-14 (detailed example from p. 10)
Aug. 11 (lecture 13)
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.