Finite Elements in Action
Modeling Quantum Mechanics and Electrodynamics in Nanoscale Systems
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Product details:
- Publisher OUP Oxford
- Date of Publication 19 March 2026
- ISBN 9780199563487
- Binding Hardback
- No. of pages528 pages
- Size 250x175x30 mm
- Weight 1152 g
- Language English
- Illustrations 189 b/w and colour illustrations 0
Categories
Short description:
Aimed at graduate students and researchers, 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.
MoreLong description:
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.
Table of Contents:
Part I - The Action Integral in Quantum Mechanics
Schrödinger's equation and the action
Action, FEM and BCs
Element geometries for 2D and 3D
Boundary conditions at material interfaces
Accidental degeneracy in cubic semiconductor quantum dots
Part II - Quantum Scattering
Quantum scattering in 1D revisited
2D quantum waveguides
Quantum scattering in 2D waveguides
Open domain quantum scattering with sources and absorbers
Part III - Wavefunction Engineering
Wavefunction engineering of semiconductor nanostructures
Schrödinger-Poisson self-consistency in layered semiconductor nanostructures
Part IV - Steady-state current distributions
The Extraordinary Magneto-Resistance effect in metal- semiconductor structures
Read-head design based on the EMR effect
Part V - Electrodynamics
Fields in electromagnetic waveguides
Modeling photonic crystals with Hermite FEM
Cavity Electrodynamics and symmetries
Dimensional continuation of EM singularities in structures with re-entrant geometry
The gauge degree of freedom in Electrodynamics
Part VI - Further applications of FEM
Derivation of shape functions using group theory
Shape functions for 1D, 2D, and 3D finite elements
Hermite Least Squares Data Fitting
