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\begin{document}

\title{Determination of the Eigenfunction's and Eigenvalue's of Quantum dots by
FDTD}



\author[1]{sedighe shanan hayavi}%
\affil[1]{Shahid Chamran University of Ahvaz}%


\vspace{-1em}



  
  \date{May 10, 2024}


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\selectlanguage{english}
\begin{abstract}
In this Article, we consider quantum dots with different structures and
solve the Schr\selectlanguage{ngerman}ödinger equations for them by finite difference
time-domain method and obtain the Eigenfunction's and the Eigenvalue's
of these points.The FDTD method have an analysis that demonstrates the
high accuracy of this method for solving quantum equations.The FDTD
method is a suitable method for simulating electromagnetic phenomena, in
this Article we present a simple formulation for the Schrödinger
equation in FDTD. In fact, we get help from the idea of FDTD and solve
quantum equations. The most important structures we have simulated with
this method are cubic quantum dot, spherical quantum dot, elliptical
quantum dot and partial truncate-shaped quantum dots on the wetting
layer. It is very difficult to solve the Schrödinger equation
analytically for these structures, but by using the numerical method we
obtain the Eigenfunction's and Eigenvalue's in a simpler way.%
\end{abstract}\selectlanguage{ngerman}%



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\textbf{Hosted file}

\verb`Article-quantum dot.docx`  available at \url{https://authorea.com/users/309251/articles/440457-determination-of-the-eigenfunction-s-and-eigenvalue-s-of-quantum-dots-by-fdtd}

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\end{document}

