Finite Element and Boundary Element Applications in Quantum Mechanics

Finite Element and Boundary Element Applications in Quantum Mechanics

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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 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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Product details

  • Paperback | 624 pages
  • 156 x 234 x 32mm | 868g
  • Oxford, United Kingdom
  • English
  • numerous figures and tables
  • 0198525222
  • 9780198525226

Table of contents

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
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Review Text

"... well structured and remarkably comprehensive..." John Pask, Lawrence Livermore National Laboratory, CA
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Review quote

"... opens new ground for physicists, particularly those interested in condensed matter physics and chemistry..."
A.K. Rajagopal, Naval Research Laboratory, Washington D.C. "... an excellent textbook to introduce FEM and BEM to students..."
Shun-Lien Chua ng, University of Illinois at Urbana-Champaign "... well structured and remarkably comprehensive..."
John Pask, Lawrence Livermore National Laboratory, CA
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