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    Analytical solution for 3D stationary Schro¨ dinger equation: implementation of Huygens’ principle for matter waves

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    Date
    2017-11-10
    Author
    Eleuch, Hichem
    Yuri V. Rostovtsevc
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    Abstract
    We have found an analytical solution of the 3D stationary Schro¨ dinger equation for any arbitrary potential. The solution has been obtained by transforming the Schro¨ dinger equation to the generalized Ricatti equation, and it has the form of Huygens’ principle for matter waves. We have shown that the solution is more accurate than the JWKB approximation. We discuss possible applications of the solution to molecular dynamics and dynamics of charges in nanostructures.
    URI
    https://dspace.adu.ac.ae/handle/1/1243
    DOI
    https://doi.org/10.1080/09500340.2010.514069
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