Cornell University
Department of Physics
Phys 480/680, Astro 690 March 1, 2005
Computational Physics, Spring 2005
Homework Assignment # 4
(Due Thu, March 3)
Agenda and readings for the week of March 1:
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:
- Lec 9, 02/22 (Tue) Recap big picture; numerical stability of
solution of ODE's, shooting to a fitting point; numerical
interpolation; Y
's and non-spherical states.
Readings: NR
17.2, 3.0-3.2
- Lec 10, 02/24 (Thu): Nomenclature for (nl)-shells in atoms;
normalization conventions and definitions for our calculations;
calculation of total energy within density functional theory;
exchange-correlation energy per particle, electron gas parameter
r
.
Readings: Sections ``Introduction,'' ``Procedure'' (you
can skip the relativistic part), ``Results,'' and ``The LDA
approximation,'' from
http://physics.nist.gov/PhysRefData/DFTdata/contents.html
- Lab 3, 02/24 (Thu): Stability of solutions, effectiveness of
root finders; convergence of eigenvalues with N.
Preview of coming week:
- Lec 11, 03/01 Solution of many non-linear equations in many unknowns
(Broyden approaches); motivation for a ``modified'' Broyden's
method; modified Broyden method; overview of numerical linear algebra
Readings: NR 9.6-9.7, 2.0
- Lec 12, 03/03 Solution of linear systems by LU decomposition;
Crout's algorithm
Readings: NR 2.3
- Lab 4, 03/03 Energies of harmonic oscillator; ``hot-wired''
solver for atoms within Hartree theory!
Tomas Arias
2005-03-01
