Centering equations under align

There are a number of ways of achieving this:

\documentclass{article}

\usepackage{amsmath,siunitx}

\begin{document}

Using \verb|align*|:
\begin{align*}
  E_n = \frac{n^2h^2}{8m_{e^{-}}L^2} & & L = 4 \times d_{\text{c-c}} = 5.64\si{\angstrom} \\
  & E_1 = \frac{1^2h^2}{8m_{e^{-}}5.46^2}
\end{align*}

Using \verb|gather*| (1):
\begin{gather*}
  E_n = \frac{n^2h^2}{8m_{e^{-}}L^2} \qquad L = 4 \times d_{\text{c-c}} = 5.64\si{\angstrom} \\
  E_1 = \frac{1^2h^2}{8m_{e^{-}}5.46^2}
\end{gather*}

Using \verb|gather*| (2):
\begin{gather*}
  E_n = \frac{n^2h^2}{8m_{e^{-}}L^2} \quad
  \phantom{E_1 = \frac{1^2h^2}{8m_{e^{-}}5.46^2}} \quad
  L = 4 \times d_{\text{c-c}} = 5.64\si{\angstrom} \\
  \phantom{E_n = \frac{n^2h^2}{8m_{e^{-}}L^2}} \quad
  E_1 = \frac{1^2h^2}{8m_{e^{-}}5.46^2} \quad
  \phantom{L = 4 \times d_{\text{c-c}} = 5.64\si{\angstrom}}
\end{gather*}

Using \verb|alignat*|:
\begin{alignat*}{3}
  E_n = \frac{n^2h^2}{8m_{e^{-}}L^2} & & L = 4 \times d_{\text{c-c}} = 5.64\si{\angstrom} \\
  & \quad E_1 = \frac{1^2h^2}{8m_{e^{-}}5.46^2} \quad
\end{alignat*}

Using an \verb|array|:
\begin{equation*}
  \renewcommand{\arraystretch}{2}
  \begin{array}{ *{3}{c} }
    \displaystyle E_n = \frac{n^2h^2}{8m_{e^{-}}L^2} & & L = 4 \times d_{\text{c-c}} = 5.64\si{\angstrom} \\
    & \displaystyle E_1 = \frac{1^2h^2}{8m_{e^{-}}5.46^2}
  \end{array}
\end{equation*}


\end{document}

You can use the alignat environment:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc} % Fontencoding: 7bit -> 8bit
\usepackage{lmodern}
\usepackage{amsmath}
\begin{document}
\begin{alignat*}{2}
E_n = \frac{n^2h^2}{8m_{e^{-}}L^2} & & L=4\times d_{\text{c-c}}=5.64\\
&E_1 = \frac{1^2h^2}{8m_{e^{-}}5.46^2}&
\end{alignat*}
\end{document}

Note, however, this will place the equation below in between the gap of the two above. It doesn't really center it. Especially, if the equation is long, there will be much space between the first equations.