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Aspects of the Modeling of Low Dimensional Quantum Systems

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Low-Dimensional and Nanostructured Materials and Devices

Part of the book series: NanoScience and Technology ((NANO))

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Abstract

The mathematical modeling of low dimensional quantum systems is discussed in this chapter. In particular, the use of generalized functions in such modeling is illustrated in some detail, including applications of the Dirac delta function and its derivative (“delta-prime”) in determining quantum mechanical Schrödinger Green’s functions describing the dynamics of various low dimensional systems. The illustrations include quantum dots, wires and wells (and a superlattice) in various dimensions. Also, the one-dimensional “delta-prime” potential is shown to provide an impenetrable barrier.

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Author information

Authors and Affiliations

  1. Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, New Jersey, 07030, USA

    Norman J. M. Horing

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  1. Norman J. M. Horing
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Correspondence to Norman J. M. Horing .

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Editors and Affiliations

  1. Department of Physics Engineering, Faculty of Science and Letters,, Istanbul Technical University, Istanbul, Türkiye

    Hilmi Ünlü

  2. Department of Physics and Engineering Physics, Stevens Institute of Technology, Hoboken, NJ, USA

    Norman J. M. Horing

  3. Leibniz-Inst. für innovative Mikroelektr, Innovations for High Performance Microelectronics (IHP) GmbH, Frankfurt, Germany

    Jaroslaw Dabrowski

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Horing, N.J.M. (2016). Aspects of the Modeling of Low Dimensional Quantum Systems. In: Ünlü, H., Horing, N.J.M., Dabrowski, J. (eds) Low-Dimensional and Nanostructured Materials and Devices. NanoScience and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-25340-4_2

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