Computer simulation is an indispensible research tool for modeling, understanding, and predicting nanoscale phenomena. There is a huge gap between the complexity of the programs and algorithms used in computational physics courses and and those used in research for computer simulations of nanoscale systems. The advanced computer codes used by researchers are often too complicated for students who want to develop their own codes, want to understand the essential details of computer simulations, or want to improve existing programs.

The aim of this book is to provide a comprehensive program library and description of advanced algorithms to help students and researchers learn novel methods and develop their own approaches. An important contribution of this book is that it is accompanied by an algorithm library in Fortran 90 that implements the computational approaches described in the text.

The physical problems are solved at various levels of sophistication using methods based on classical molecular dynamics, tight binding, density functional approaches, or fully correlated wave functions. Various basis functions including finite differences, Lagrange functions, plane waves, and Gaussians are introduced to solve bound state and scattering problems and to describe electronic structure and transport properties of materials. Different methods of solving the same problem are introduced and compared.

The book is divided into two parts. In the first part we concentrate on one-dimensional problems.