Cornell University

Department of Physics

Phys 480/680, Astro 690 February 22, 2006

Computational Physics, Spring 2006

Homework Assignment # 4

(Due Wed, March 1)

Agenda and readings for the week of February 27:

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$^{\mathrm nd}$ 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 8 02/16 (Thu) Secant/False Position method; Ridders method
  Reading: NR 9.2

• Lab 2 02/16 (Thu) Convergence of solution of ODE's; numerical solutions of Schrödinger's equation.

• Lec 9, 02/21 (Tue) Numerical interpolation; Numerical stability of solution of ODE's, shooting to a fitting point; Y$_{lm}$'s and Non-spherical states (higher angular momenta).
  Readings: NR 17.2, 3.0-3.2.

• Lec 10, 02/23 (Thu): Non-spherical states cont'd, 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$_s$; Functional form for exchange-correlation energy.
  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, 02/23 (Thu): Effectiveness of root finders; convergence of eigenvalues with N.

Preview of coming week:

• Lec 11, 02/28 Solution of many non-linear equations in many unknowns (Broyden approaches); motivation for a ``modified'' Broyden's method
  Readings: NR 9.6-9.7, 2.0

• Lec 12, 03/02 Modified Broyden method

• Lab 4, 03/02 Energies of harmonic oscillator; ``hot-wired'' solver for atoms within Hartree theory!

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