Cornell University

Department of Physics

Phys 480/680, Astro 690 April 12, 2007

Computational Physics, Spring 2007

Homework Assignment # 8

(Due Wednesday, April 18 at 5:00pm)

Agenda and readings:

Goals: Implement variational solution to Schrödinger's equation and Kohn-Sham equations using steepest descents.

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:

• 04/10 Lec 19 (Tue) DFT++ expressions for energy and gradient for multiple states and for density functional theory
  Reading: Sections 1-4 of http://arxiv.org/abs/cond-mat/9909130

• 04/12 Lec 20 (Thu) Converge of steepest descents; preconditioning; preview of improved minimization methods
• 04/12 Lab 7 (Thu) Spectral solution of Poisson's equation

Preview:

• 04/17 Lec 21 (Tue) Details behind line minimization; motivation for conjugate gradients; begin conjugate gradient algorithm
  Reading: NR 10.2, 10.3. 10.5, 10.6
• 04/19 Lec 22 (Thu) Finish conjugate gradients
  Reading: NR 12.2
• 04/19 Lab 8 (Thu) Spectral solution of Schrödinger's equation

• 04/24 Lec 23 (Tue) FFT; Further optimizations for spectral methods; ab initio pseudopotentials
  Reading: 12.2
• 04/26 Lec 24 (Thu) Extraction of eigenstates from variational principle
• 04/26 Lab 9 (Thu) Performance of numerical minimization techniques; preconditioner for quantum calculations

• 05/02 Lec 25 (Tue) TBD
• 05/04 Lab 10 (Thu) Physics of harmonic oscillator, H2 molecule and germanium solid

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