Finite Element and Boundary Element Applications in Quantum Mechanics

This book introduces the finite element and boundary element methods (FEM & BEM) for applications to quantum mechanical systems. A discretization of the action integral with finite elements, followed by application of variational principles, brings a very general approach to the solution of Schroedinger's equation for physical systems in arbitrary geometries with complex mixed boundary conditions. The variational approach is a common thread through the book and is used for the improvement of solutions to spectroscopic accuracy, to adaptively improve finite element meshs, to develop a time-dependent theory, and also to generate the solution of large sparse matrix eigenvalue problems. A thorough introduction to BEM is given using the modelling of surface plasmons, quantum electron waveguides, and quantum scattering as illustrative examples. The book should be useful to graduate students and researchers in basic quantum theory, quantum semiconductor modeling, computational physics, mathematics and chemistry.

1 - Introduction
2 - Simple quantum systems
3 - Interpolation polynomials in 1D
4 - Adaptive FEM
5 - Quantum mechanical tunneling
6 - Schrödinger-Poisson self-consistency
7 - Landau states in a magnetic field
8 - Wavefunction engineering
9 - 2D Elements and shape functions
10 - Mesh Generation
11 - Applications in atomic physics
12 - Quantum wires
13 - Quantum waveguides
14 - Time dependent problems
15 - Matrix solvers and related issues
16 - The boundary element method
17 - BEM and surface plasmons
18 - BEM and quantum applications
A - Gaussian quadrature
B - Generalized functions
C - Green's functions
D - Physical constants