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Numerical Calculations of the Quantum States in Semiconductor Nanostructures

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Abstract:

In this review we describe the use of a powerful numerical tool to obtain quantum states of semiconductor nanostructures. A detailed account of the numerical method is given and the method is applied to solve the Schrödinger equation for several semiconductor systems within the effective mass approximation. The variety of systems investigated shows how flexible and effective the method is. The scheme for the calculation of the eigenvalues and eigenvectors is a modified version of a split-operator approach to propagate the wave functions by infinitesimal time steps, applied both in real and imaginary time propagations. Interesting aspects in this modified approach are the use of real space coordinates, time propagation in real and imaginary domains, the treatment of excited states as well as of systems with interacting particles.

Keywords: COMPUTATIONAL TECHNIQUES; EXCITONS; SEMICONDUCTOR NANOSTRUCTURES; TRIONS

Document Type: Review Article

DOI: https://doi.org/10.1166/jctn.2010.1380

Publication date: 2010-02-01

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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