Finite Elements in Action: Modeling Quantum Mechanics and Electrodynamics in Nanoscale Systems

The central focus of this textbook is the elucidation of the interplay between the principle of stationary action and Schrödinger's equation, and its solution using the finite element method (FEM), a method of solving differential equations, in physical systems whose dimensions are on the order of nanometers. The treatment of the dynamics of electrons in such systems deserves a quantum mechanical description and typical applications at the nanoscale also require the modeling of electrodynamic fields. For instance, nanoscale semiconductor laser design requires the interplay between electrons and photons to be modeled simultaneously.

Aimed at graduate students and researchers in nanoscale systems, materials growth, optoelectronics, engineering, physics, and chemistry, as well as electrical engineers, mechanical engineers, computational scientists, and quantum computer developers, this book explores the development of variational methods and their implementation for several physical examples in the framework of the FEM and addresses issues that are very common in modeling nanoscale systems.

L. Ramdas Ram-Mohan, Director, Center for Computational NanoScience (CCNS), Worcester Polytechnic Institute

L. Ramdas Ram-Mohan graduated from St. Stephen's College at Delhi University with a B.Sc. (Honors) in 1964 and did his graduate work at Purdue University in theoretical high energy physics earning his MS and PhD in 1971. After post-doctoral assignments at the Freie Universität in Berlin and Delhi University, he joined Purdue University from 1975 to 1978. He has been at Worcester Polytechnic Institute since 1978 as Assistant, Associate, and was made Full Professor in 1985. His interests have ranged from quantum field theory, linear and nonlinear optical properties of semiconductor heterostructures, to high-accuracy finite element methods for scattering theory and electrodynamics, band structures of solids, and wavefunction engineering of quantum well lasers.