Chowdhury, Sujaul. creator author. aut http://id.loc.gov/vocabulary/relators/aut Talukder, Urmi. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) text sz 2024 1st ed. 2024. monographic eng

electronic

electronic resource

access VIII, 91 p. 69 illus. online resource. 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. Background on Microelectronics -- Background on Semiconductor Nanostructure Physics -- Numerical Calculation of Energy Spectrum of GaAs-AlGaAs Quantum Well Having Abrupt Potential Steps Using Regula Falsi Method -- Numerical calculation of Energy Spectrum of GaAs-AlGaAs Quantum Well Having Abrupt Potential Steps Using Finite Difference Method -- Numerical Calculation of Energy Spectrum of Parabolic Quantum Well of Finite Depth Using Finite Difference Method. by Sujaul Chowdhury, Urmi Talukder. Semiconductors Nanoscience Nanotechnology Mathematical physics Physics Semiconductors Nanophysics Nanometrology Mathematical Methods in Physics Applied and Technical Physics Nanoengineering QC610.9-611.8 9783031538162 https://doi.org/10.1007/978-3-031-53816-2 https://doi.org/10.1007/978-3-031-53816-2 240422 20251030112003.0 978-3-031-53816-2