\input{preamble}
\input{format}
\input{commands}
\begin{document}
\begin{Large}
\textsf{\textbf{This is a great title}}
This is an even greater subtitle
\end{Large}
\vspace{1ex}
\textsf{\textbf{Student:}} \text{Your name}, \href{mailto:your.email@hotmail.com}{\texttt{your.email@hotmail.com}}\\
\textsf{\textbf{Lecturer:}} \text{Teacher's name}, \href{mailto:teacher.email@hotmail.com}{\texttt{teacher.email@hotmail.com}}
\vspace{2ex}
Here I show a very basic example of how to use the \textquote{\texttt{problem}} environment I defined using the \verb|\tcolorbox| package. You can define your own environments following the problem environment in the \texttt{format.tex} file.
\begin{problem}{Your title}{problem-label}
This is an example problem taken from \cite{Sakurai2020}:
\begin{enumerate}[(a)]
\item Prove the following
\begin{enumerate}[label = (\roman*)]
\item $\langle p' | x | \alpha \rangle = \im \hbar \pdv{}{p'} \langle p' | \alpha \rangle$.
\item $\langle \beta | x | \alpha \rangle = \int \dd{p'} \phi_{\beta}^{*} (p') \im \hbar \pdv{}{p'} \phi_{\alpha} (p'),$
where $\phi_{\alpha}(p') = \langle p' | \alpha \rangle$ and $\phi_{\beta}(p') = \langle p' | \beta \rangle$ are momentum-space wave functions.
\end{enumerate}
\item What is the physical significance of
\[
\exp\left(\dfrac{\im x \Xi}{\hbar}\right),
\]
where $x$ is the position operator and $\Xi$ is some number with the dimension of momentum? Justify your answer.
\end{enumerate}
\end{problem}
Notice that the partial derivative and integral are smaller when used in a sentence compared with when you're working in a math environment like \verb|\begin{equation} \end{equation}|. If you want to display the full size of such commands in a sentence, you must use the command \verb|\displaystyle{}|, like it's shown here:
\begin{problem}{Your title}{problem-label-2}
This is an example problem taken from \cite{Sakurai2020}:
\begin{enumerate}[(a)]
\item Prove the following
\begin{enumerate}[label = (\roman*)]
\item $\langle p' | x | \alpha \rangle = \im \hbar \displaystyle{\pdv{}{p'} }\langle p' | \alpha \rangle$.
\item $\langle \beta | x | \alpha \rangle = \displaystyle{\int \dd{p'} \phi_{\beta}^{*} (p') \im \hbar \pdv{}{p'} \phi_{\alpha} (p')}$,
\vspace{1ex}
where $\phi_{\alpha}(p') = \langle p' | \alpha \rangle$ and $\phi_{\beta}(p') = \langle p' | \beta \rangle$ are momentum-space wave functions.
\end{enumerate}
\item $\cdots$
\end{enumerate}
\end{problem}
I use the package \texttt{physics} which provides a great variety of commands for common operations and symbols. For instance, instead of typing \verb|\dfrac{\partial x}{\partial t}|, the \texttt{physics} package provides the command \verb|\pdv{x}{t}| which gives the same result. I also defined my own commands, so you can take a look in the \texttt{commands.tex} file if you like. I'd also suggest to create a folder and work each problem in a separate \texttt{.tex} file. I already included such folder in the \texttt{Overleaf} template, but you won't see it if you download the \texttt{Github} template.
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