Cornell University

Department of Physics

Phys 480/680, Astro 690 April 26, 2007

Computational Physics, Spring 2007

Homework Assignment # 9

(Due Wednesday, April 25 at 5:00pm)

Agenda and readings:

Goal: Predict bond length of H$_2$ molecule!

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:

• 04/17 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; finite difference test, finite difference derivative and machine precision; begin extraction of eigenstates from variational principle
  Reading: NR 12.2
• 04/19 Lab 8 (Thu) Spectral solution of Schrödinger's equation

Preview of final weeks of class:

• 04/24 Lec 23 (Tue) Finish extraction of eigenstates from variational principle; FFT; Further optimizations for spectral methods
  Reading: 12.2
• 04/26 Lec 24 (Thu) ab initio pseudopotentials
• 04/26 Lab 9 (Thu) Performance of numerical minimization techniques; preconditioner for quantum calculations; physics of simple harmonic oscillator and quantum dot; physics of H2 molecule.

• 05/01 Lec 25 (Tue): Theoretical background for density functional theory
• 05/03 Lab 10 (Thu): Physics of germanium solid and final discussion

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