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Quantum Dot and Acoustic Enclosure Problems in Lens-Shaped Structures

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Computational Science and Its Applications — ICCSA 2003 (ICCSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2668))

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Abstract

A method for solving exactly the Helmholtz equation in parabolic rotational coordinates is presented using separability of the eigenfunctions and the Frobenius power series expansion technique. Two examples of interest in wave physics are considered and analyzed quasianalytically: (I) the wavefunctions of an electron in a quantum dot confined by two paraboloids (forming a lens-shaped structure) and the associated energy spectrum, and (II) the acoustic eigenmodes and eigenfrequencies of the pressure field bounded by rigid walls as defined by two paraboloids. The quantum dot (acoustic enclosure) problem is a Dirichlet (Neumann) boundary condition problem. In both cases, eigenfunctions and eigenmodes are calculated and the shape-dependence of the first eigenvalue for the groundstate in the quantum dot case (and the fundamental mode in the acoustic enclosure case) is examined.

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Author information

Authors and Affiliations

  1. Mads Clausen Institute, University of Southern Denmark, DK-6400, Denmark

    M. Willatzen

  2. Department of Physics, Worcester Polytechnic Institute, MA, 01609, USA

    L. C. Lew Yan Voon

Authors
  1. M. Willatzen
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  2. L. C. Lew Yan Voon
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Editor information

Editors and Affiliations

  1. Army High Performance Computing Research Center, USA

    Vipin Kumar

  2. Department of Computer Science and Engineering, University of Minessota, MN, 55455, USA

    Vipin Kumar

  3. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  4. Heuchera Technologies Inc., 122 9251-8 Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  5. School of Computer Science, The Queen’s University of Belfast, Belfast, BT7 1NN, Northern Ireland, UK

    Chih Jeng Kenneth Tan

  6. Département d’informatique et de recherche opérationelle, Université de Montréal, Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

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© 2003 Springer-Verlag Berlin Heidelberg

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Willatzen, M., Yan Voon, L.C.L. (2003). Quantum Dot and Acoustic Enclosure Problems in Lens-Shaped Structures. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2668. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44843-8_80

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  • DOI: https://doi.org/10.1007/3-540-44843-8_80

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40161-2

  • Online ISBN: 978-3-540-44843-3

  • eBook Packages: Springer Book Archive

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