How can I write an equation with two curly brackets?

Question

I am trying to write this equation.

I used these commands:

\begin{eqnarray}\label{eqn1}
|1, \:\: \:1\rangle &=& \uparrow \uparrow   \nonumber \\
|1, \:\:\: 0\rangle &=& \frac{1}{\sqrt{2}}\big(\uparrow \downarrow + \downarrow\uparrow \big) \\
|1, -1\rangle &=& \downarrow \downarrow   \nonumber \\ \nonumber
\end{eqnarray}

But how can I add the two curly brackets?

Answer 1

How about this?

\documentclass{article}
\begin{document}
\begin{equation}
  \label{eqn1}
\setlength{\arraycolsep}{0pt}
  \left\{
\begin{array}{lcl}
|1, \phantom{-}1\rangle &{}={}& \uparrow \uparrow \\
|1, \phantom{-}0\rangle &=& \frac{1}{\sqrt{2}}\big(\uparrow \downarrow + \downarrow\uparrow \big) \\
|1, -1\rangle &=& \downarrow \downarrow 
\end{array}
\right\}
\end{equation}
\end{document}

Answer 2

Never use eqnarray.

Your particular alignment can be obtained with alignedat; the argument 2 means that we want two pairs of right/left aligned columns. We leave empty the right aligned columns so to emulate two left aligned columns.

\documentclass{article}
\usepackage{amsmath}
\newcommand{\foo}[2]{\mathopen|{#1}\ {#2}\rangle}
\newcommand{\uua}{{\uparrow}{\uparrow}}
\newcommand{\uda}{{\uparrow}{\downarrow}}
\newcommand{\dua}{{\downarrow}{\uparrow}}
\newcommand{\dda}{{\downarrow}{\downarrow}}
\begin{document}
\begin{equation}\label{eqn1}
\left{
\begin{alignedat}{2}
  &\foo{1}{1}  &&= \uua \
  &\foo{1}{0}  &&= \frac{1}{\sqrt{2}}\bigl(\uda + \dua\bigr) \
  &\foo{1}{-1} &&= \dda
\end{alignedat}
\right}
\end{equation}
\end{document}

Choose a better name for \foo, based on the name of the symbol. All the braces I used in the definitions are important.

As an aside, avoid labeling like eqn1: use a string that describes the equation.

You may want \tfrac instead of \frac and the output would be

If you need combinations of the arrows (any number of them), you can use

\documentclass{article}
\usepackage{amsmath}
\newcommand{\foo}[2]{\mathopen|{#1}\ {#2}\rangle}
\ExplSyntaxOn
\NewDocumentCommand{\AR}{m}
 {
  \str_map_inline:nn { #1 }
   {
    \str_case:nn { ##1 } { {u}{{\uparrow}} {d}{{\downarrow}} }
   }
 }
\ExplSyntaxOff
\begin{document}
\begin{equation}\label{eqn1}
\left{
\begin{alignedat}{2}
  &\foo{1}{1}  &&= \AR{uu} \
  &\foo{1}{0}  &&= \tfrac{1}{\sqrt{2}}\bigl(\AR{ud} + \AR{du}\bigr) \
  &\foo{1}{-1} &&= \AR{dd}
\end{alignedat}
\right}
\end{equation}
\end{document}

The output is the same, but you can do

\[
\AR{u}\quad
\AR{d}\quad
\AR{uu}\quad
\AR{uduudd}
\]

to get

Answer 3

With Bmatrix* defined in mathtools:

\documentclass[border=3.14,varwidth]{standalone}
\usepackage{mathtools}
\begin{document}
\begin{equation}\label{eqn1}
    \setlength\arraycolsep{1pt}
\begin{Bmatrix}[r]
|1, & 1\rangle  =& \uparrow\uparrow & \
|1, & 0\rangle  =& \frac{1}{\sqrt{2}}& !\bigl(\uparrow \downarrow + \downarrow\uparrow \bigr) \
|1, & -1\rangle =& \downarrow\downarrow &
\end{Bmatrix}
\end{equation}
\end{document}

Answer 4

Another idea it is to use braket package with newcommand to predefinite symbols of Table 142 of the documentation The Comprehensive LATEX Symbol List and with a style that it is similar to the first image: you see the packages

\usepackage{newtxtext,newtxmath}

You will have:

\documentclass[a4paper,12pt]{article}
\usepackage{mathtools,amssymb}
\usepackage{newtxtext,newtxmath}
\usepackage{graphicx}
\usepackage{braket}
\newcommand{\uupa}{\rotatebox[origin=c]{90}{$\rightleftarrows$}}
\newcommand{\dupa}{\rotatebox[origin=c]{90}{$\leftrightarrows$}}
\begin{document}
[\Set{\begin{array}{lcl}
\Ket{1, 1}  & = & \upuparrows\
\Ket{1, 0}  & = & \frac{1}{\sqrt{2}}(\uupa+\dupa) \
\Ket{1, -1}  & = & \downdownarrows 
\end{array}}]
\end{document}

Remember that the \Set command give a bit of spaces to left and the right the curly bracket.