Cornell University

Department of Physics

Phys 480/680, Astro 690 April 23, 2004

Computational Physics, Spring 2004

Homework Assignment # 8

(Due Thursday, April 29)

Agenda and readings for the weeks of April 6-23:

Goals: Solution of single particle Schrödinger equation using unconstrained minimization techniques; minimization using steepest descents; solution of the harmonic oscillator in $d=3$ dimensions.

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 two weeks of class:

• 04/13 Lec 18: Details of implementation of spectral methods: mappings to d=3 dimensions, Aliasing/Nyquist frequency, Fourier factorization theorem
  Reading: NR 12.0, 12.4

• 04/15 NO CLASS
• 04/16 NO LAB
• 04/20 Lec 19: Fourier inversion theorem; variational principle for eigenvalue problems in $d>1$ dimension

• 04/22 Lec 20: Analytic continuation for constrains; algebraic formulation for energy for Schrödinger's equation; Numerical minimization: steepest descents
  Reading: NR 10.0

• 04/23 NO LAB

Preview of final two weeks:

• 04/27 Lec 21: Numerical minimization: line minimization, preconditioning; difficulties with line minimization; concept of conjugate gradients (directions, actually)
  Reading: NR 10.6

• 04/29 Lec 22: Conjugate gradient algorithm

• 04/30 Lab 8: Spectral solution to Poisson's equation in octave, solution to Schrödinger's equation via steepest descent minimization

• 05/04 Lec 23: Derivation of gradients in algebraic notation, gradients for DFT

• 05/06 Lec 24: FFT algorithm

• 05/07 Lab 9: DFT solutions for molecules

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