main.tex

\documentclass{article}
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\title{Equations}
\author{Patrick Dobranowski, Xylo Molenda}

\begin{document}

\maketitle

\section{Equations}

\begin{equation}
\begin{aligned}
    \langle \alpha_{ij} | 0, z \rangle = \sum_{n=0}^{\infty} e^{-\frac{|\alpha_{ij}|^2}{2}} \frac{(\alpha_{ij}^*)^{2n} (-1)^n}{2^n n!} \left( \frac{e^{i \theta} \tanh r}{\sqrt{\cosh r}} \right)^n
\end{aligned}
\end{equation}

\begin{equation}
\begin{aligned}
    i \hbar \dot{C}_{i'j'k'n'} = \sum_{ij} \left( E_u + (|\alpha_{ij}|^2 + nN) \hbar \omega \right) C_{ijk'n'} + \sum_{ijk} i \epsilon_w \langle A_u' | D | A_u \rangle (\alpha_{ij}^* + \alpha_{ij}) C_{ijkn'} + \sum_{ijk} i \epsilon_{Nw} \langle A_u' | D | A_u \rangle \sqrt{n'} C_{ijk,n'-1} + \sum_{ijk} i \epsilon_{Nw} \langle A_u' | D | A_u \rangle \sqrt{n'+1} C_{ijk,n'+1}
\end{aligned}
\end{equation}

\end{document}