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% Edit these as appropriate
\newcommand\course{CHEM 446/337}
\newcommand\hwnumber{1} % <-- homework number
\newcommand\MyName{Gilbert Gottfried} % <-- Your Name
\newcommand\MyID{gxg123} % <-- Your NetworkID
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\begin{document}
% Start solutions here
\section{Integrals}
\subsection{Gaussian}
\begin{equation}
\int_{-\infty}^{\infty} dx e^{-\alpha x^2} = \sqrt{\frac{\pi}{\alpha}}
\end{equation}
\subsection{Trig functions}
Use \verb|\begin{align*}...\end{align}| for derivations.
\begin{align*}
\int_0^\pi \cos(x) \cos(3x) dx & = \\
& = \int_0^\pi \frac{1}{2}\left(\cos(4x) + \cos(2x)\right) dx \\
& = \frac{1}{2(4}\sin(4x)\Big|^\pi_0 + \frac{1}{2(2)}\sin(2x)\Big|^\pi_0 \\
& = 0
\end{align*}
\section{Linear Algebra}
\begin{equation}
\mathbf{H} = \begin{pmatrix}
E_0 & V \\
V & E_1
\end{pmatrix}
\end{equation}
\section{Quantum Mechanics}
\begin{equation}
\hat{H}|\Psi(t)\rangle = i \frac{\partial}{\partial t}|\Psi(t)\rangle
\end{equation}
\end{document}
