Separable Boundary-Value Problems in Physics
1st Edition
Published on 10. May 2011
XXI, 377 pages
978-3-527-63494-1 (ISBN)
Description
Accessible and comprehensive treatment of partial differential equations in a variety of coordinate systems and geometry, and their solutions using the method of separation of variables. With problems and modern examples from nanotechnology and other fields of physics.
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M. Willatzen
Separable Boundary-Value Problems in Physics
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04/2011
Wiley-VCH
€173.48
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Morten Willatzen | Lok C. Lew Yan Voon
Separable Boundary-Value Problems in Physics
Book
04/2011
Wiley-VCH
€125.00
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Persons
Morten Willatzen is Head of Research at the Center for Product Innovation of the Mads Clausen Institute at the University of Southern Denmark. Having received his PhD from the Niels Bohr Institute at the University of Copenhagen, he held positions at Aarhus University, Max-Planck-Institute for Solid State Research, Germany, and Senior Scientist at Danfoss A/S, DK. In 2000 he became Associate Professor, in 2004 Full Professor at the University of Southern Denmark. Morten Willatzen's research interests include solid state physics, in particular quantum-confined structures and applications to semiconductor laser amplifiers, flow acoustics, and modelling of thermo-fluid systems.
L. C. Lew Yan Voon is Professor and Chair of the Department of Physics at Wright State University. Educated in Cambridge, England, and Vancouver, Canada, he received his PhD from Worcester Polytechnic Institute, USA, where he held positions until 2004, with a stay at the Max-Planck-Institute for Solid State Research as an Alexander von Humboldt fellow. Dr. Lew Yan Voon was visiting scientist at the Air Force Research Laboratory, Hong Kong University of Science and Technology, Stanford University, and the University of Southern Denmark. Professor Lew Yan Voon received the Balslev Award (Denmark) and the NSF CAREER award. His research interests are in semiconductor theory and mathematical physics and involve the study of band structure theory and applications to nanostructures.
L. C. Lew Yan Voon is Professor and Chair of the Department of Physics at Wright State University. Educated in Cambridge, England, and Vancouver, Canada, he received his PhD from Worcester Polytechnic Institute, USA, where he held positions until 2004, with a stay at the Max-Planck-Institute for Solid State Research as an Alexander von Humboldt fellow. Dr. Lew Yan Voon was visiting scientist at the Air Force Research Laboratory, Hong Kong University of Science and Technology, Stanford University, and the University of Southern Denmark. Professor Lew Yan Voon received the Balslev Award (Denmark) and the NSF CAREER award. His research interests are in semiconductor theory and mathematical physics and involve the study of band structure theory and applications to nanostructures.
Content
Part I Preliminaries
1. Introduction
2. General Theory
Part II Two-Dimensional Coordinate Systems
3. Rectangular Coordinates
4. Circular Coordinates
5. Elliptic Coordinates
6. Parabolic Coordinates
Part III Three-Dimensional Coordinate Systems
7. Rectangular Coordinates
8. Circular Cylinder Coordinates
9. Elliptic Cylinder Coordinates
10. Parabolic Cylinder Coordinates
11. Spherical Polar Coordinates
12. Prolate Spheroidal Coordinates
13. Oblate Spheroidal Coordinates
14. Parabolic Rotational Coordinates
15. Conical Coordinates
16. Ellipsoidal Coordinates
17. Paraboloidal Coordinates
Part IV Advanced Formulations
18. Differential Geometric Formulations
19. Quantum-mechanical Particle Confined to Neighborhood of Curves
20. Quantum-mechanical Particle Confined to Surfaces of Revolution
21. Boundary Perturbation Theory
Appendices
A Hypergeometric Functions
B Baer Functions
C Bessel Functions
D Lamé Functions
E Legendre Functions
F Mathieu Functions
G Spheroidal Wave Functions
H Weber Functions
I Elliptic Integrals and Functions
Index
1. Introduction
2. General Theory
Part II Two-Dimensional Coordinate Systems
3. Rectangular Coordinates
4. Circular Coordinates
5. Elliptic Coordinates
6. Parabolic Coordinates
Part III Three-Dimensional Coordinate Systems
7. Rectangular Coordinates
8. Circular Cylinder Coordinates
9. Elliptic Cylinder Coordinates
10. Parabolic Cylinder Coordinates
11. Spherical Polar Coordinates
12. Prolate Spheroidal Coordinates
13. Oblate Spheroidal Coordinates
14. Parabolic Rotational Coordinates
15. Conical Coordinates
16. Ellipsoidal Coordinates
17. Paraboloidal Coordinates
Part IV Advanced Formulations
18. Differential Geometric Formulations
19. Quantum-mechanical Particle Confined to Neighborhood of Curves
20. Quantum-mechanical Particle Confined to Surfaces of Revolution
21. Boundary Perturbation Theory
Appendices
A Hypergeometric Functions
B Baer Functions
C Bessel Functions
D Lamé Functions
E Legendre Functions
F Mathieu Functions
G Spheroidal Wave Functions
H Weber Functions
I Elliptic Integrals and Functions
Index
