Home Page for Computational Physics 2007

(Cornell Phys 480, Phys 680 and Astro 690)

Announcements:

• None at this time.

Office Hours

• Prof. Arias office hours: 522 Clark Hall, Mon 10:15-11:15am
• TA office hours: 604 Clark Hall, time TBD

Important links

• Books and original articles on density-functional theory:
  • Books:
    • Density-Functional Theory of Atoms and Molecules (International Series of Monographs on Chemistry, No 16) by Robert G. Parr, Weitao Yang.
    • A Chemist's Guide to Density Functional Theory, 2nd Edition, by Wolfram Koch, Max C. Holthausen.
  • Original articles:
    • "Inhomogeneous Electron Gas," by P. Hohenberg and W. Kohn, Physical Review 136, B864-B871 (1964).
    • "Self-Consistent Equations Including Exchange and Correlation Effects," by W. Kohn and L. J. Sham, Physical Review 140, A1133-A1138 (1965).
    • "Correlation Energy of an Electron Gas at High Density," by M. Gell-Mann and K.A. Brueckner, Physical Review 106, 364-368 (1957).
    • "New algebraic formulation of density functional calculation,'' by Sohrab Ismail-Beigi and T.A. Arias, Computer Physics Communications 128:1-2, 1-45 (June 2000).

• Free versions of Numerical Recipes on line
  • 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".

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

• On-line Hartree-Fock calculator

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].

• 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; Ewald summation of nuclear-nuclear interaction in periodic systems
  [HTML Postscript PDF ]

• Problem Set # 8: Spectral solution of eigenvalue problems; steepest descents; solution of Schrodinger's equation and Kohn-Sham equations in three dimensions; solution of simple harmonic oscillator and quantum dot,
  [HTML Postscript PDF ]

• Problem Set # 9: Line minization, preconditioning, conjugate gradients; Computation of the bond-length of the hydrogen molecule, with your own code built from scratch!!!
  [HTML Postscript PDF ]

• Problem Set # 10 (last one!!!): Computation of the binding energy and electron distribution in the bonds of a germanium crystal, again with your own code built from scratch!!!
  [HTML Postscript PDF ]