Cornell University
Department of Physics
Phys 480/680, Astro 690 February 27, 2004
Computational Physics, Spring 2002
Homework Assignment # 4
(Due Thu, March 11)
Agenda and readings for the week of February 26:
Goal: This homework develops and packages into subroutines the
functionality needed to perform complete calculations for atoms.
Readings marked NR are from Numerical Recipes: The Art of
Scientific Computing, 2
edition (in C). Readings
marked LN are from the course lecture notes to be found at
http://www.muchomas.lassp.cornell.edu/P480.
Recap of last week:
- Lec9, 02/24 (Tue) Secant method; Ridders method; bracketing of roots for Schrödinger's equation
Reading: NR 9.2
- Lec10, 02/26 (Thu): Shooting to a fitting point; normalization conventions for atoms; Non-spherical states (higher angular momenta)
- Lab3, 02/27 (Fri): Stability of solutions, effectiveness of root finders; convergence of eigenvalues with N.
Preview of coming week:
- 03/02 NO LECTURE
- 03/04 Numerical interpolation; exchange and correlation energy
functionals; solution of many non-linear equations in many unknowns
(Broyden approaches); our need for a ``Modified'' Broyden's Method
Readings: NR 3.0-3.2, 9.6-9.7; Sections ``Introduction,''
``Procedure'' (you can skip the relativistic part), ``Results,''
and ``The LDA approximation,'' from
http://physics.nist.gov/PhysRefData/DFTdata/contents.html
- 05/05 NO LAB
- 03/09 Relations among self-consistent iteration, charge mixing,
and Broyden's method; line optimization, full, modified Broyden's
method
- 03/11 Introduction to Numerical linear algebra; benefits of
LAPACK/ATLAS; Analysis of convergence of charge mixing; condition
numbers
Tomas Arias
2004-02-27
