Home Page for Computational Physics 2004

(Cornell Phys 480, Phys 680 and Astro 690)

Announcements: (none at present)

Course Hours

• Prof. Arias office hours: 522 Clark Hall, Tue 3-4pm
• TA office hours: Rock B3, Wed 4:40-5:30pm
• Problem set check-off hours: Rock B3, Thu 12-1pm, 3-4pm.
• Lab: Rock B3, Fri 8:00-8:50am

Important links

• US National Institute of Standards and Technology project on the electronic structure of atoms

• On-line Hartree-Fock calculator

• Cornell's access to Numerical Recipes for free!

• Numerical Recipes book on line!

• Cut and paste versions of Numerical Recipes utilities and header file

• On-line version of "What Every Computer Scientist Should Know About Floating-Point Arithmetic".

Class Handouts

Course Information
[HTML Postscript PDF ]

Lecture Notes

• Overview of quantum mechanics of material systems (density functional theory)
  [ HTML, Postscript, PDF ]

• Numerical Integration of functions
  [HTML, Postscript, PDF ]

Animations

• Animation of integration of the one-dimensional Schrodinger equation as a function of energy
  [HTML/MPEG]

  This movie is from a web based quantum mechanics course which has a variety of other interesting animations.

Problem Sets

• Problem Set # 1: Numerical integration --- potential energy terms in atoms
  [HTML Postscript PDF ]
  Solutions: [Postscript, PDF].

• Problem Set # 2: Solution of ODE's --- Poisson's equation in atoms and a simple Schrondinger solver
  [HTML Postscript PDF ]
  Solutions: [Postscript, PDF].

• Problem Set # 3: Root finding -- Automated, high precision Schrodinger solver for energies of atomic states
  [HTML Postscript PDF ]
  Solutions: [Postscript, PDF].

• Problem Set # 4: Matching method; packaging -- Automated, high precision Schrodinger solver for wave functions of atoms; full set of routines needed for self-consistent atomic calculations
  [HTML Postscript PDF ]
  Solutions: [Postscript, PDF].

  Compiling hint for Problem Set 4:
  The grader hit some issues in getting his code to compile. If you are having problems, you may want to try the following: When copying from the "nrutil.c" file to "p480.c", there are two versions of the tensor routines; make sure to copy the ANSI versions (they were first in his file). To compile, he needed to copy the macro lines

  #define NR_END 1
  #define FREE_ARG char*

  that are needed by free_d3tensor(). He also needed to add the header file

  #include <stddef.h>

  to define "size_t" in d3tensor().

• Problem Set # 5: Exchange and correlation energy functionals; implementation of self-consistency; density functional theory of atoms
  [HTML Postscript PDF ]
  Solutions: [Postscript, PDF].

• Problem Set # 6: Optimization of atomic code, FLOP counting of inner loop operations, cache optimization, ATLAS LAPACK, Octave --
  [HTML Postscript PDF ]
  Solutions: [Postscript, PDF].

• Problem Set # 7: Spectral solution of PDE's; expressive software: Poisson's equation in a single line of octave code.
  [HTML Postscript PDF ]

• Problem Set # 8 (Due April 29): Solution of Schrodinger's equation in three dimensions using spectral methods and steepest descents
  [HTML Postscript PDF ]

• Problem Set # 9 (Due May 6): line minization, preconditioning, conjugate gradientsl computation of the bond-length of the hydrogen molecule, with your own code built from scratch!!!
  [HTML Postscript PDF ]

  Errata for Problem Set #9

  • The form for the effective potential in Eq. (9) should be
    Vsc=gbl_Vdual +cJdag(O(phi)) +cJdag(O(cJ(excVWN(n)))) +excpVWN(n).*cJdag(O(cJ(n)));
  • The final form for the total energy in Eq. (7) should be
    -gbl_f*0.5*trace(Y'*L(Y)) +gbl_Vdual'*n +0.5*n'*cJdag(O(phi)) +cJ(excVWN(n))'*O(cJ(n));
  • The formula for the Polak-Ribiere form should be
    beta=real(trace((g-og)'*K(g)))/real(trace((og-g)'*K(og)));
  • The formula for beta in the Hestenes-Stiefel version of conjugate-gradients had a factor of "K" in the denominator which should not be there. Please re-down load the problem set (You may have to hit "reload" on your browser in case the file is buffered.) to see the proper formula or simply delete the "K" in the denominator only.