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Numerical Exploration of Isolated GaAs-AlGaAs Quantum Well (Synthesis Lectures on Engineering, Science, and Technology) - Hardcover
Synopsis
This book begins with the eigenvalue equation of energy and presents calculation of the energy spectrum of GaAs-AlGaAs Quantum Well using finite difference method and knowledge of potential energy profile, without using expressions for eigenfunctions, continuity of eigenfunctions, or their spatial derivatives at the two abrupt potential steps. The authors find that the results are almost the same as those obtained by solving numerically using regula falsi method, and transcendental equations that are obeyed by the energy levels, where the transcendental equations are obtained by requiring continuity of eigenfunctions and of their spatial derivatives at the two potential steps. Thus, this book confirms that it is possible to numerically calculate the energy spectrum of Quantum Well by the finite difference method when it is not correct or when it is not possible to use continuity of eigenfunctions and their spatial derivatives at the two abrupt potential steps. The authors also showthat it is possible to use the finite difference method in cases where the potential steps are non-abrupt. The book demonstrates this by calculating the energy spectrum of isolated parabolic Quantum Well of finite depth using finite difference method.
"synopsis" may belong to another edition of this title.
About the Author
Sujaul Chowdhury, Ph.D., is a Professor in the Department of Physics at Shahjalal University of Science and Technology. He received his B.Sc. and M.Sc. in Physics from Shahjalal University of Science and Technology, before earning his Ph.D. at The University of Glasgow in 2001. He is the author of many books, including Monte Carlo Methods: A Hands-On Computational Introduction Utilizing Excel; Monte Carlo Methods Utilizing Mathematica®: Applications in Inverse Transform and Acceptance-Rejection Sampling; Numerical Exploration of Fourier Transform and Fourier Series: The Power Spectrum of Driven Damped Oscillators; and Newtonian Mechanics.
Urmi Talukder is an M.S. student in Department of Physics at Shahjalal University of Science and Technology.
From the Back Cover
This book begins with the eigenvalue equation of energy and presents calculation of the energy spectrum of GaAs-AlGaAs Quantum Well using finite difference method and knowledge of potential energy profile, without using expressions for eigenfunctions, continuity of eigenfunctions, or their spatial derivatives at the two abrupt potential steps. The authors find that the results are almost the same as those obtained by solving numerically using regula falsi method, and transcendental equations that are obeyed by the energy levels, where the transcendental equations are obtained by requiring continuity of eigenfunctions and of their spatial derivatives at the two potential steps. Thus, this book confirms that it is possible to numerically calculate the energy spectrum of Quantum Well by the finite difference method when it is not correct or when it is not possible to use continuity of eigenfunctions and their spatial derivatives at the two abrupt potential steps. The authors also show that it is possible to use the finite difference method in cases where the potential steps are non-abrupt. The book demonstrates this by calculating the energy spectrum of isolated parabolic Quantum Well of finite depth using finite difference method.
In addition, this book:
- Presents innovative research on alternative methods of calculating the energy spectrum of GaAs-AlGaAs Quantum Well
- Includes confirmation of the authors’ results by comparing them to the standard calculation techniques
- Highlights the opportunities for further use of the finite difference method in nanostructure physics
"About this title" may belong to another edition of this title.
- PublisherSpringer
- Publication date2024
- ISBN 10 3031538153
- ISBN 13 9783031538155
- BindingHardcover
- LanguageEnglish
- Number of pages99
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Numerical Exploration of Isolated GaAs-AlGaAs Quantum Well
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -This book begins with the eigenvalue equation of energy and presents calculation of the energy spectrum of GaAs-AlGaAs Quantum Well using finite difference method and knowledge of potential energy profile, without using expressions for eigenfunctions, continuity of eigenfunctions, or their spatial derivatives at the two abrupt potential steps. The authors find that the results are almost the same as those obtained by solving numerically using regula falsi method, and transcendental equations that are obeyed by the energy levels, where the transcendental equations are obtained by requiring continuity of eigenfunctions and of their spatial derivatives at the two potential steps. Thus, this book confirms that it is possible to numerically calculate the energy spectrum of Quantum Well by the finite difference method when it is not correct or when it is not possible to use continuity of eigenfunctions and their spatial derivatives at the two abrupt potential steps. The authors also showthat it is possible to use the finite difference method in cases where the potential steps are non-abrupt. The book demonstrates this by calculating the energy spectrum of isolated parabolic Quantum Well of finite depth using finite difference method. 112 pp. Englisch. Seller Inventory # 9783031538155
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Numerical Exploration of Isolated GaAs-AlGaAs Quantum Well
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - This book begins with the eigenvalue equation of energy and presents calculation of the energy spectrum of GaAs-AlGaAs Quantum Well using finite difference method and knowledge of potential energy profile, without using expressions for eigenfunctions, continuity of eigenfunctions, or their spatial derivatives at the two abrupt potential steps. The authors find that the results are almost the same as those obtained by solving numerically using regula falsi method, and transcendental equations that are obeyed by the energy levels, where the transcendental equations are obtained by requiring continuity of eigenfunctions and of their spatial derivatives at the two potential steps. Thus, this book confirms that it is possible to numerically calculate the energy spectrum of Quantum Well by the finite difference method when it is not correct or when it is not possible to use continuity of eigenfunctions and their spatial derivatives at the two abrupt potential steps. The authors also showthat it is possible to use the finite difference method in cases where the potential steps are non-abrupt. The book demonstrates this by calculating the energy spectrum of isolated parabolic Quantum Well of finite depth using finite difference method. Seller Inventory # 9783031538155
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Numerical Exploration of Isolated GaAs-AlGaAs Quantum Well
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Buch. Condition: Neu. Neuware -This book begins with the eigenvalue equation of energy and presents calculation of the energy spectrum of GaAs-AlGaAs Quantum Well using finite difference method and knowledge of potential energy profile, without using expressions for eigenfunctions, continuity of eigenfunctions, or their spatial derivatives at the two abrupt potential steps. The authors find that the results are almost the same as those obtained by solving numerically using regula falsi method, and transcendental equations that are obeyed by the energy levels, where the transcendental equations are obtained by requiring continuity of eigenfunctions and of their spatial derivatives at the two potential steps. Thus, this book confirms that it is possible to numerically calculate the energy spectrum of Quantum Well by the finite difference method when it is not correct or when it is not possible to use continuity of eigenfunctions and their spatial derivatives at the two abrupt potential steps. The authors also showthat it is possible to use the finite difference method in cases where the potential steps are non-abrupt. The book demonstrates this by calculating the energy spectrum of isolated parabolic Quantum Well of finite depth using finite difference method.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 112 pp. Englisch. Seller Inventory # 9783031538155
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