Graduate Seminar Course Math 285J:

Mathematical Aspects of Computational Materials Science



Handouts

Handout from Jan. 9; Multiscale Modeling
Derivation of Hartree-Fock equations, Jan. 23

References

The following books and articles have been used to prepare my lectures
In particular, I note in blue certain sections that have been used for particular lectures.

Lectures on many body quantum mechanics and electronic structure calculations (DFT and Hartree Fock):
  • J.M. Thijssen, "Computational Physics", Cambridge University Press, 1999.
    Lecture 3, 4, Jan. 14, 16, Hartree Fock and CI: Used 4.1, 4.2, 4.4, 4.5.
    Lecture on Feb. 11, 13, Molecular Dynamics and Monte Carlo: Used 8.1, 8.2, 8.5, and 10.1, 10.2, 10.3

  • R.O. Jones, and O. Gunnarsson, Review of Modern Physics 61, 689 (1989), The Density Functional Formalism, its Applications and Prospects.
    I think that this is an excellent review and introduction to density functional theory. I used the first 12 pages.

  • Szabo and Ostlund, "Modern Quantum Chemistry; Introduction to Advanced Electronic Structure Theory", Dover publications, 1982.
    Lecture 3, 4, Jan. 14, 16, Hartree Fock and CI: Used Section 2, pages 40-60.

  • Dreizler and Gross, "Density Functional Theory", Springer.

  • J.J. Sakurai, "Modern Quantum Mechanics", Addison-Wesley, 1985.
    Lecture 2, Jan. 9: Used chapter 1, pages 1 - 40.


    • Lectures on Molecular Dynamics and KMC:
  • J.M. Thijssen, "Computational Physics", Cambridge University Press, 1999.
    Lecture on Feb. 11, 13, Molecular Dynamics and Monte Carlo: Used 8.1, 8.2, 8.5, and 10.1, 10.2, 10.3


    • Lectures on Rate Equations, 2-25-02:
  • many books/articles, but I have not used any particular one. Please ask me if you want further references


    • Lecture on Continuum Equations, 2-27-02:
  • J. Villain, J. Phys. I 1, 19 (1991).
  • A good reference book is A. Pimpinelli and J. Villain, "Physics of Crystal Growth", Cambridge University Press, 1998.
    I used chapters 8, 12, 13, 14.


    • Lectures on Level Set Method, 3-4-02:
  • Ongoing research in our group. Check out Web page on materials research in Applied Math at UCLA.