Books on Eigenvalue Problem

Solutions of many physical systems involve finding eigenvalues and eigenvectors. For large systems, iterative methods are often used instead of exact diagonalization method. I think these books may be useful for you if you want to learn and solve large eigenvalue problems.

Iterative methods for sparse linear systems (1st edition) and Numerical Methods for Large Eigenvalue Problems by Yousef Saad. Both can be read at http://www-users.cs.umn.edu/~saad/books.html

A practical guide to computer simulations

I just stumbled upon a useful article which explains concisely how to do computer simulation from programming to visualization.

http://arxiv.org/abs/cond-mat/0111531
A practical guide to computer simulations
abstract:
Here practical aspects of conducting research via computer simulations are discussed. The following issues are addressed: software engineering, object-oriented software development, programming style, macros, make files, scripts, libraries, random numbers, testing, debugging, data plotting, curve fitting, finite-size scaling, information retrieval, and preparing presentations.
Because of the limited space, usually only short introductions to the specific areas are given and references to more extensive literature are cited. All examples of code are in C/C++.

Computational-Physics Resources

A new article by Rubin H. Landau appeared in American Journal of Physics contains many resources for Computational Physics. I think you should read it!. It has many useful information for students and teachers to do physical simulations. Other articles in the same journal I also found them very interesting!.

Rubin H. Landau (2008): Resource Letter CP-2: Computational Physics,
American Journal of Physics, Volume 76, Issue 4, pp. 296-306
Abstract:
This Resource Letter provides a guide to print and electronic literature relevant to a computational physics course. The multidisciplinary aspect of computational physics and its relation to computational science is reflected in the sections Courses, Programs and Reviews, Journals, Conferences and Organizations, Books, Tools, Languages and Environments, Parallel Computing, and Digital Libraries.

Handbook of Mathematical Functions

For simulations of many physical systems, one might encounter problems that require the use of special functions and mathematical formula. I found the book by Abramowitz and Stegun "Handbook of Mathematical Functions" is very useful. An electronic copy of the tenth printing of this book can be found in the following link:
http://www.math.sfu.ca/~cbm/aands/

Solving Schrodinger Equation and Computing Density Matrix

I have written two papers about the finite difference time domain (FDTD) method for solving the Schroedinger equation and for computing the single particle density matrix. I have put these papers in the arXiv.org.

[1] arXiv:0712.4317
Title: The Finite Difference Time Domain Method for Computing Single-Particle Density Matrix
Authors: I. Wayan Sudiarta, D. J. Wallace Geldart
Comments: 19 pages, 8 figures

[2] arXiv:0712.4201
Title: Solving the Schrodinger Equation for a Charged Particle in a Magnetic Field using the Finite Difference Time Domain Method
Authors: I. Wayan Sudiarta, D. J. Wallace Geldart
Comments: 8 pages, 4 figures