Finite Element and Boundary Element Applications in Quantum Mechanics
Author: Ramdas Ram-Mohan Series: Oxford Texts in Applied and Engineering Mathematics
Part 1: Introduction to FEM 1. Introduction 2. Simple quantum systems 3. Interpolation polynomials in 1D 4. Adaptive FEM Part 2: 1D Applications 5. Quantum mechanical tunneling 6. Schrodinger-Poisson self-consistency 7. Landau states in a magnetic field 8. Wavefunction engineering Part 3: 2D Applications of FEM 9. 2D Elements and shape functions 10. Mesh Generation 11. Applications in atomic physics 12. Quantum wires 13. Quantum waveguides 14. Time dependent problems Part 4: Sparse matrix applications 15. Matrix solvers and related issues Part 5: Boundary elements 16. The boundary element method 17. BEM and surface plasmons 18. BEM and quantum applications Part 6: Appendices A. Gaussian quadrature B. Generalized functions C. Green's functions D. Physical constants
Starting from a clear, concise introduction, the powerful finite element and boundary element methods of engineering are developed for application to quantum mechanics. The reader is led through illustrative examples displaying the strengths of these methods using applications to fundamental quantum mechanical problems and to the design/simulation of quantum nanoscale devices.
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Summary
Part 1: Introduction to FEM 1. Introduction 2. Simple quantum systems 3. Interpolation polynomials in 1D 4. Adaptive FEM Part 2: 1D Applications 5. Quantum mechanical tunneling 6. Schrodinger-Poisson self-consistency 7. Landau states in a magnetic field 8. Wavefunction engineering Part 3: 2D Applications of FEM 9. 2D Elements and shape functions 10. Mesh Generation 11. Applications in atomic physics 12. Quantum wires 13. Quantum waveguides 14. Time dependent problems Part 4: Sparse matrix applications 15. Matrix solvers and related issues Part 5: Boundary elements 16. The boundary element method 17. BEM and surface plasmons 18. BEM and quantum applications Part 6: Appendices A. Gaussian quadrature B. Generalized functions C. Green's functions D. Physical constants
Starting from a clear, concise introduction, the powerful finite element and boundary element methods of engineering are developed for application to quantum mechanics. The reader is led through illustrative examples displaying the strengths of these methods using applications to fundamental quantum mechanical problems and to the design/simulation of quantum nanoscale devices.
Description
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 bookand 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 matrixeigenvalue 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
Critic Reviews
“"... well structured and remarkably comprehensive..."John Pask, Lawrence Livermore National Laboratory, CA”
"... an excellent textbook to introduce FEM and BEM to students..."Shun-Lien Chua ng, University of Illinois at Urbana-Champaign"... opens new ground for physicists, particularly those interested in condensed matter physics and chemistry..."A.K. Rajagopal, Naval Research Laboratory, Washington D.C.
About the Author
Ramdas Ram-Mohan is a Professor of Physics and Electrical and Computer Engineering, Worcester Polytechnic Institute, USA.
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
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