Eigenstate Calculations for Multidimensional Nanostructures: Quantum Wells, Wires and Dots

Nanotechnology is the latest buzzword in scientific circles. Fabrication of new nanoscale devices calls for extremely accurate simulation and analysis. Traditional mesh based methods have been used in many CAD tools, however dealing with atomic/molecular dimensions poses new and complex problems which reveal the shortcomings of the conventional methods, mostly the mesh generation step. Recently a new category of numerical methods, called meshless methods has shown great promise in overcoming these problems by eliminating the mesh generation step. This book is intended primarily for research scientists and professionals with an interest in application of numerical methods in engineering and science. The text starts by covering the fundamentals of quantum mechanics and compares two broad categories of numerical methods used to solve partial differential equations. The book continues by describing how to use a particular meshless method to solve the multidimensional Schrodinger equation. The Schrodinger equation is solved for one-particle nanostructures with an arbitrary potential profile.