Latex Variables and if statement to show or hide code

Question

I would like to define a document, in which I define variables at the beginning of the document and use them in the document to define, from which parts of the code, the pdf is created.

This is the code and I write in * * , how I would do it in python.

\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\title{A test file}

\begin{document}
\maketitle

*Show_first_line = True*
*Show_second_line = False*

\section{Density functional theory}

*if Show_first_line == True: #Now the following formula should be compiled* 
     $$
     i \hbar \frac{\partial \Phi(\mathbf{r}, \mathbf{R} ; t)}{\partial t}=\left(-\frac{\hbar^{2}}{2 M} \frac{\partial^{2}}{\partial \mathbf{R}^{2}}-\frac{\hbar^{2}}{2 m} \frac{\partial^{2}}{\partial \mathbf{r}^{2}}+V(\mathbf{r}, \mathbf{R})\right) \Phi(\mathbf{r}, \mathbf{R} ; t)
     $$
*else:*
     $$
     i \hbar \frac{\partial \Phi(\mathbf{r}, \mathbf{R} ; t)}{\partial t}=\left( -\frac{\hbar^{2}}{2 m} \frac{\partial^{2}}{\partial \mathbf{r}^{2}}+V(\mathbf{r}, \mathbf{R})\right) \Phi(\mathbf{r}, \mathbf{R} ; t)
     $$

*if Show_second_line == True # In case it is false, nothing should be compiled*
     $$
     \mathrm{M} \gg \mathrm{m} \text { the Born-Oppenheimer approximation }
     $$

$$
i \hbar \frac{\partial \Phi(\mathbf{r}, \mathbf{R} ; t)}{\partial t}=
\left( -\frac{\hbar^{2}}{2 m} \frac{\partial^{2}}{\partial \mathbf{r}^{2}}+V(\mathbf{r}, \mathbf{R})\right) \Phi(\mathbf{r}, \mathbf{R} ; t)
$$

$$
M \ddot{\mathbf{R}}=-\frac{\partial E(\mathbf{R})}{\partial \mathbf{R}} \\
\left(-\frac{\hbar^{2}}{2 m} \frac{\partial^{2}}{\partial \mathbf{r}^{2}}+V(\mathbf{r}, \mathbf{R})\right) \Psi(\mathbf{r} | \mathbf{R})=E(\mathbf{R}) \Psi(\mathbf{r} | \mathbf{R})
$$

\end{document}

Answer 1

Welcome to TeX.SE! The following variation on this answer should do what you want:

\documentclass{article}
\usepackage{environ}
\usepackage{etoolbox}

% The toggles are initially false
\newtoggle{showfirstline}
\newtoggle{showsecondline}

\toggletrue{showfirstline}
\togglefalse{showsecondline}    % useless here

% Uncomment this if you don't want spaces after \end{maybePrint} to be
% discarded (the default is \environfinalcode{\ignorespacesafterend}, which
% causes such spaces to be ignored):
%
%\environfinalcode{}

\NewEnviron{maybePrint}[1]{%
  \iftoggle{#1}{\BODY}{}%
}

\begin{document}

\begin{maybePrint}{showfirstline}
  \[ \frac{\pi^2}{6} = \sum_{n=1}^{+\infty} \frac{1}{n^2}  \]
\end{maybePrint}

\begin{maybePrint}{showsecondline}
  \[ a^2 = b^2 + c^2 \]
\end{maybePrint}

Other text.

\end{document}

Note: don't use $$ ... $$ for display formulas with LaTeX, prefer \[ ... \] (see Why is \[ … \] preferable to $$ … $$?).