Cornell University

Department of Physics

Phys 480/680, Astro 690 February 27, 2007

Computational Physics, Spring 2006

Homework Assignment # 4

(Due Mon, March 5 at 5:00pm)

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 02/20 (Tue) Analysis of convergence of secant method; Ridders method.
  Reading: NR 9.2

• Lab 2 02/20 (Tue) IEEE arithmetic; convergence of solution of ODE's; numerical solutions of Schrödinger's equation; numerical stability.

• Lec 9, 02/22 (Thu) Numerical stability of solution of ODE's, shooting to a fitting point; Numerical interpolation; Y$_{lm}$'s and Non-spherical states (higher angular momenta).
  Readings: NR 17.2, 3.0-3.2.

• Lec 10, 02/27 (Tue): 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.

• Lab 3, 02/27 (Tue): Effectiveness of root finders; convergence of eigenvalues with N; rescaling of linear solutions to handle machine overflow.

Preview of coming week:

• Lec 11, 03/01 (Thu) Exchange-correlation energy per particle, electron gas parameter r$_s$; Functional form for exchange-correlation energy; 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; Sections ``Introduction,'' ``Procedure'' (you can skip the relativistic part), ``Results,'' and ``The LDA approximation,'' from
  http://physics.nist.gov/PhysRefData/DFTdata/contents.html .

• Lec 12, 03/06 (Tue) Modified Broyden method

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

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