main.tex

\documentclass[twoside]{article}
\usepackage{Quill}

\addbibresource{bibliography.bib} % Comment to remove bibliography

\begin{document}
\init{Quill template example: simple usage}{Author Name}{Student Code / Empty if not provided}{Affiliation \& Location (Contact information)}

\abstract{This is the Abstract section. This part here should contain all the relevant information about your project. This should \textbf{ALWAYS} come before any paragraph. This project uses the font \textit{libertinus}, if you prefer the normal font simply comment the use package libertinus line in the style file. Mathematics expressions are styled using normal latex font. You can change that uncommenting the math-libertinus line. To display your custom logo on the header, the correct path is \texttt{\underline{Images/Template/Logo.png}}. The suggested dimension is 320x320 or 256x256; you might need, however, to manually adapt your image by changing the \texttt{\underline{headrule}} command. First change the scale of the image and later the vertical spacing, until the horizontal line adapts correctly to the text.} 

\begin{pcontext}
    \begin{paragraph}{Introduction}
        This is an introduction to the actual text. To use double column paragraphs, you should initialize a context, using the custom \texttt{\underline{pcontext}} environment. An equation is displayed using either \texttt{\underline{equation}} or \texttt{\underline{align}}:
        \begin{align}
            \hat{H}\psi = E\psi\,.
        \end{align}
        In case you want to use colored boxes, one should use an appropriate environment, depending on the length of the equation you want to display. You can use the \texttt{\underline{coleq}}, \texttt{\underline{coleqgath}} environments to display the equations:
        \begin{coleq}
            \left[-\frac{\hbar^2}{2m}\nabla^2 + V(\bvec{x})\right]\psi(\bvec{x}) = E\psi(\bvec{x})\,.
        \end{coleq}
        Bold vectors are displayed using the \texttt{\underline{bvec[x]}} command. Note that colored environments are already displayed using spacing above and below the paragraph, whereas normal AMS environments are not. Using an asterisk in colored environments name removes the number on the right of the equation. There are some custom-made commands to fasten mathematical writing, for example \texttt{\underline{pder[func][var]}}, provides a wrapper for a partial derivative, whereas \texttt{\underline{qstate[func]}} provides a wrapper for Dirac's quantum state notation, like in the example of Equation (\ref{eq:Schrodinger}):
        \begin{align}\label{eq:Schrodinger}
             i\hbar\pder{\qstate{\psi}}{t} = \left[-\frac{\hbar^2}{2m}\nabla^2 + V(\bvec{x})\right]\qstate{\psi}\,.
        \end{align}
        Other custom commands include \texttt{\underline{RR}}, \texttt{\underline{CC}}, \texttt{\underline{QQ}}, \texttt{\underline{AA}}, \texttt{\underline{HH}}, \texttt{\underline{ZZ}}, \texttt{\underline{II}}, \texttt{\underline{PP}},
        \texttt{\underline{NN}} for blackboard-bold lettering (number sets), \texttt{\underline{innp[a][b]}} for dot products, \texttt{\underline{qinnp[a][b]}} for Dirac notation dot product and \texttt{\underline{qoutp[a][b]}} for Dirac notation outer product:
        \begin{align}
            \int_\RR d\lambda \,\, \qoutp{\lambda}{\lambda} = \mathbf{1}\,. 
        \end{align}
        The commands \texttt{\underline{series[idx][expr]}} and\\ \texttt{\underline{sseries[idx][start][expr]}} allows to write a series using the $\geq$ notation. The first command should be used when the series starts from 0, like in the following example:
        \begin{align}
            & \series{n}{\frac{1}{2^n}} = 2\,. \\
            & \sseries{n}{1}{\frac{1}{n^2}} = \frac{\pi^2}{6}\,.
        \end{align}
    \end{paragraph}
    \begin{paragraph}{Images and Tables}
        Images are scaled to fit in a column specifying \texttt{width=\textbackslash linewidth} in the \texttt{includegraphics} settings. If the image is not found at the specified path, a squared border will appear.:
        \begin{figure}[H]
            \centering
        \includegraphics[width=\linewidth]{Images/Template/Logo.png}
            \caption{Your picture should appear here.}
            \label{fig:example} 
        \end{figure}\noindent
        If you are writing a lab report, it might be useful to display data using tables. The \texttt{\underline{Quill}} template provides a colored environment for tables, using the \texttt{\underline{coltab}} environment. Here I provide two examples of the same table:
        \begin{coltab}
        \centerline{
        \begin{NiceTabular}{r||lll}[hvlines]
        i & $\mathcal{W}_{AC}$~~~~[mJ]&  $\mathcal{W}_{\mathrm{Tot}}$~~~~[mJ]& $\mathcal{W}_{AC} / \mathcal{W}_{\mathrm{Tot}}$\\
        \hline\hline
            1 & 9.1 $\pm$\:0.4 & 13.68 $\pm$\:0.07& 0.67 $\pm$\:0.03\\
             2 & 8.8 $\pm$\:0.4& 13.22 $\pm$\:0.07 & 0.66 $\pm$\: 0.03\\
             3 & 6.1 $\pm$\:0.4& 10.94 $\pm$\: 0.06& 0.58 $\pm$\: 0.03\\
             \hline
        \end{NiceTabular}
        }
        \captionof{table}
        {Table of measurements in a \texttt{\underline{coltab}} environment.}
        \end{coltab}
        \begin{center}
        \centerline{
        \begin{NiceTabular}{r||lll}[hvlines]
        i & $\mathcal{W}_{AC}$~~~~[mJ]&  $\mathcal{W}_{\mathrm{Tot}}$~~~~[mJ] & $\mathcal{W}_{AC} / \mathcal{W}_{\mathrm{Tot}}$\\
        \hline\hline
            1 & 9.1 $\pm$\:0.4 & 13.68 $\pm$\:0.07& 0.67 $\pm$\:0.03\\
             2 & 8.8 $\pm$\:0.4& 13.22 $\pm$\:0.07 & 0.66 $\pm$\: 0.03\\
             3 & 6.1 $\pm$\:0.4& 10.94 $\pm$\: 0.06& 0.58 $\pm$\: 0.03\\
             \hline
        \end{NiceTabular}
        }
        \captionof{table}
        {Table of measurements in a plain environment.}
        \end{center}
        To obtain the second result, simply wrap the table in a \texttt{\underline{center}} environment. There are no default tables provided by this template, so you should create your own every time, leaving complete freedom in the styling process.
    \end{paragraph}
    \begin{paragraph*}{Anonymous paragraph}
        You can use the anonymous paragraph, using an asterisk after the \texttt{\underline{paragraph}} environment. This will hide the roman numeral before the section title.
        \begin{subparagraph*}{Anonymous subparagraph}
        This works on sub-paragraphs too using the \texttt{\underline{subparagraph*}} environment.
        \end{subparagraph*}
    \end{paragraph*}
    \begin{paragraph}{Longer equations}\label{sec:longeq}\noindent
    Sometimes, most equation might not fit within a column. To avoid this problem, you have to close the \texttt{\underline{pcontext}} after closing the \texttt{\underline{paragraph}}, and later reopen the paragraph using an anonymous section with a blank title:
    \end{paragraph}
\end{pcontext}
    \begin{align}
        {}_2F_1(a,b,c;z)
= \frac{\Gamma(c)}{\Gamma(b)\,\Gamma(c-b)}
\int_0^1 dt\,\,t^{\,b-1}\,(1-t)^{\,c-b-1}\,(1-zt)^{-a}\,.
    \end{align}
    \begin{coleq}
        {}_2F_1(a,b,c;z)
= \frac{\Gamma(c)}{\Gamma(b)\,\Gamma(c-b)}
\int_0^1 dt\,\,t^{\,b-1}\,(1-t)^{\,c-b-1}\,(1-zt)^{-a}\,.
    \end{coleq}
\begin{pcontext}
    \begin{paragraph*}{}
    Paragraph (\ref{sec:longeq}) continues here on left. Fun fact: the equations above display the integral representation of one of the six branches of the hypergeometric function, the power series solution to the differential equation:
    \begin{align}\label{eq:hypdiff}
        z(1-z)\,u'' + [c - (a + b +1)z]\,u' -ab\,u = 0\,.
    \end{align}
    This solution is valid as long as $|z|<1$, and it represents the solution around the Fuchsian point $z=0$, obtained via the Frobenius-series method. The hypergeometric function plays an important role in many areas of Mathematics and Physics such as Quantum Mechanics, in fact, Equation (\ref{eq:hypdiff}) allows to generalize many differential equations, including the differential equations associated to orthogonal polynomials. Applying the transformation $z \rightarrow z/b$ and in the limit as $b\rightarrow +\infty$ one gets the \textbf{confluent hypergeometric equation}, which defines the \textbf{confluent hypergeometric function}\footnote{Also known as \textbf{Kummer's function}. It satisfies the property: $\Phi(a,c;z) = \underset{b\rightarrow+\infty}{\lim}{}_2F_1(a,b,c;z/b)$.} $\Phi(a,c;z)$, extending the class of functions that can be represented.
    \end{paragraph*}
    \begin{paragraph}{Citations and Bibliography}
        Citations works using the \texttt{\underline{cite}} command. The \texttt{\underline{hyperref}} package will automatically link the citation to the bibliography reference, allowing dynamic-referencing within the document. Here is an example, citing \textbf{Attention is all you need} \cite{vaswani2023attentionneed}. Use the \texttt{\underline{printbibliography}} command to display the bibliography. As a personal suggestion, always print the bibliography within \texttt{\underline{pcontext}} if you are using the multi-columned layout. 
    \end{paragraph}
    \printbibliography
\end{pcontext}
\begin{paragraph*}{Appendix}
    You can also use paragraphs outside the \texttt{\underline{pcontext}} environment. This will result in a single column document, providing great flexibility. I hope you will find this template useful and a valid choice among other similar templates, given the vast flexibility and customization that this template offers. You can see the full list of commands by accessing the \texttt{\underline{quill.sty}} file.
\end{paragraph*}

\end{document}