%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%           SPINS 2 from Oregon State University                %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\documentclass[12pt]{article}
% colors
\usepackage[dvipsnames,svgnames,x11names]{xcolor}
% graphics
\usepackage{graphics}
% TikZ picture environment
\usepackage{tikz}
\usetikzlibrary{arrows,scopes,fadings}
% Math formatting
\usepackage{amsmath}
% More math
\usepackage[fleqn,tbtags]{mathtools}
% Physics symbols
\usepackage{physics}
%\usepackage{mdwlist}
% tables
\usepackage{tabularx}
    \newcolumntype{L}[1]{>{\hsize=#1\hsize\raggedright\arraybackslash}X}%
    \newcolumntype{R}[1]{>{\hsize=#1\hsize\raggedleft\arraybackslash}X}%
    \newcolumntype{C}[1]{>{\hsize=#1\hsize\centering\arraybackslash}X}%
%Page Margins
\usepackage{geometry}
\geometry{top=1.5in,left=1in, right=1in, bottom = 1.5in}
% Useful commands
	% Answer in write up
	\newcommand{\ans}[1]{\textbf{\color{Black} #1}}
	% Write up on the board
	%\newcommand{\board}[1]{\textbf{\color{Red} #1}}
	% ask question
	%\newenvironment{question}{\begin{quotation} \noindent \textbf{\color{Blue} Question}\:\:}{\end{quotation}}
	%\newcommand{\ask}[2]{\begin{quotation} \noindent {\color{Blue} \textbf{Question:}\:\: #1} \\ {\color{Purple} #2}\end{quotation}}
	% answer
	%\newcommand{\ans}[1]{{\color{Purple} #1}}
	
% Vectors
	\renewcommand{\vec}[1]{\boldsymbol{#1}}
	\newcommand{\unitvec}[1]{\boldsymbol{\hat{#1}}}
\begin{document}
\title{SPINS Lab 2}
\author{Quantum Mechanics}
\date{Fall 2020}
\maketitle
\section*{Table templates}
	{ \large Unknown state $\ket{\psi_1}$}
	
	\vspace{3mm}
	
	\renewcommand{\arraystretch}{2}
	\begin{tabularx}{\textwidth}{ |c|C{1}|C{1}|C{1}| }
		\hline
        Probabilities & \multicolumn{3}{c|}{Axis} \\
		\hline
		Result & $x$ & $y$ & $z$ \\ \hline
		Spin up &&& \\ \hline
		Spin down  &&& \\ \hline
	\end{tabularx}
	\vspace{1cm}
	
	{ \large Unknown state $\ket{\psi_2}$}
	
	\vspace{3mm}
	
	\renewcommand{\arraystretch}{2}
	\begin{tabularx}{\textwidth}{ |c|C{1}|C{1}|C{1}| }
		\hline
        Probabilities & \multicolumn{3}{c|}{Axis} \\
		\hline
		Result & $x$ & $y$ & $z$ \\ \hline
		Spin up &&& \\ \hline
		Spin down  &&& \\ \hline
	\end{tabularx}
	\vspace{2cm}
	
	{ \large Unknown state $\ket{\psi_3}$}
	
	\vspace{3mm}
	
	\renewcommand{\arraystretch}{2}
	\begin{tabularx}{\textwidth}{ |c|C{1}|C{1}|C{1}| }
		\hline
        Probabilities & \multicolumn{3}{c|}{Axis} \\
		\hline
		Result & $x$ & $y$ & $z$ \\ \hline
		Spin up &&& \\ \hline
		Spin down  &&& \\ \hline
	\end{tabularx}
	\vspace{1cm}
	
	{ \large Unknown state $\ket{\psi_4}$}
	
	\vspace{3mm}
	
	\renewcommand{\arraystretch}{2}
	\begin{tabularx}{\textwidth}{ |c|C{1}|C{1}|C{1}| }
		\hline
        Probabilities & \multicolumn{3}{c|}{Axis} \\
		\hline
		Result & $x$ & $y$ & $z$ \\ \hline
		Spin up &&& \\ \hline
		Spin down  &&& \\ \hline
	\end{tabularx}
	\vspace{1cm}
	
	{ \large State $\ket{\psi}$ with magnet $B$ = {\makebox[4cm]{\hrulefill}}}
	
	\vspace{3mm}
	
	\renewcommand{\arraystretch}{2}
	\begin{tabularx}{\textwidth}{ |c|C{1}|C{1}|C{1}| }
		\hline
        Probabilities & \multicolumn{3}{c|}{Axis} \\
		\hline
		Result & $x$ & $y$ & $z$ \\ \hline
		Spin up &&& \\ \hline
		Spin down  &&& \\ \hline
	\end{tabularx}
	\vspace{2cm}
	
	{ \large Spin 1/2 Interferometer}
	
	\vspace{3mm}
	
\begin{tabularx}{\textwidth}{|C{1}|C{1}|C{1}|C{1}|C{1}|C{1}|}
		        \hline
		        \multicolumn{2}{|C{2}|}{Beams used} & \multicolumn{2}{C{2}|}{Theory} & \multicolumn{2}{C{2}|}{Experiment} \\
		        SG1 & SG2 & $\mathcal{P}_+$ & $\mathcal{P}_-$ & $\mathcal{P}_+$ & $\mathcal{P}_-$ \\ \hline
		        & $\ket{+}_x$ &&&& \\ \cline{2-6}
		        $\ket{+}$ & $\ket{-}_x$ &&&& \\ \cline{2-6}
		        & $\ket{+}_x, \, \ket{-}_x$ &&&& \\ \hline
		        & $\ket{+}_x$ &&&& \\ \cline{2-6}
		        $\ket{-}$ & $\ket{-}_x$ &&&& \\ \cline{2-6}
		        & $\ket{+}_x, \, \ket{-}_x$ &&&& \\ \hline
		    \end{tabularx}
\end{document}