5

My code is shown below, every equation is left aligned, my problem is that the equations inside the array enviroment seem to be indented. How can I align all the equations to the same vertical line?

\documentclass[letterpaper,10 pt,two column,fleqn]{article}
\setlength{\columnsep}{2.5cm}
\usepackage[inner=2.5cm,outer=2.5cm,bottom=2.5cm,top=2.5cm,landscape]{geometry}
\usepackage{nopageno,array,graphicx,amsbsy,amsfonts}
\usepackage{amsmath,MnSymbol,wasysym,bbold}
\newcommand{\ket}[1]{|{#1}\rangle}

\begin{document}
\[S_z\ket{\pm} = \pm\frac{\hbar}{2}\ket{\pm}\]
\[S_{\pm} = S_x\pm S_y\]
  \[\begin{array}{ll}
    S_z = \dfrac{\hbar}{2}(\ket{+}\bra{+} + \ket{-}\bra{-}) \mbox{\hspace{10mm}}& \ket{s_z,\pm} = \ket{\pm}\\ \\
    S_y = \dfrac{-i\hbar}{2}(\ket{+}\bra{-} - \ket{-}\bra{+}) &\ket{s_y,\pm} = \dfrac{1}{\sqrt{2}}(\ket{+}\pm i\ket{-})\\ \\ 
    S_x = \dfrac{\hbar}{2}(\ket{+}\bra{-} + \ket{-}\bra{+}) & \ket{s_x,\pm} = \dfrac{1}{\sqrt{2}}(\ket{+}\pm\ket{-})\\
  \end{array}\]
\end{document}
3

Use @{} as in \begin{array}{@{}ll}.

\documentclass[letterpaper,10 pt,two column,fleqn]{article}
\setlength{\columnsep}{2.5cm}
\usepackage[inner=2.5cm,outer=2.5cm,bottom=2.5cm,top=2.5cm,landscape]{geometry}
\usepackage{nopageno,array,graphicx,amsbsy,amsfonts}
\usepackage{amsmath,MnSymbol,wasysym,bbold,physics}
%\newcommand{\ket}[1]{|{#1}\rangle}

\begin{document}
\[S_z\ket{\pm} = \pm\frac{\hbar}{2}\ket{\pm}\]
\[S_{\pm} = S_x\pm S_y\]
  \[\begin{array}{@{}ll}
    S_z = \dfrac{\hbar}{2}(\ket{+}\bra{+} + \ket{-}\bra{-}) \mbox{\hspace{10mm}}& \ket{s_z,\pm} = \ket{\pm}\\ \\
    S_y = \dfrac{-i\hbar}{2}(\ket{+}\bra{-} - \ket{-}\bra{+}) &\ket{s_y,\pm} = \dfrac{1}{\sqrt{2}}(\ket{+}\pm i\ket{-})\\ \\
    S_x = \dfrac{\hbar}{2}(\ket{+}\bra{-} + \ket{-}\bra{+}) & \ket{s_x,\pm} = \dfrac{1}{\sqrt{2}}(\ket{+}\pm\ket{-})\\
  \end{array}\]
\end{document}

enter image description here

As a side note, instead of defining \ket and \bra, you may opt to use physics package that offers many enhancements.

3

You never want to use consecutive display math environments.

Use align:

\documentclass[letterpaper,10pt,twocolumn,fleqn]{article}

\usepackage{amsmath,braket}

\begin{document}
\begin{align*}
S_z\ket{\pm} &= \pm\frac{\hbar}{2}\ket{\pm} \\
S_{\pm} &= S_x\pm S_y \\
S_z &= \dfrac{\hbar}{2}(\ket{+}\bra{+} + \ket{-}\bra{-})
  & \ket{s_z,\pm} &= \ket{\pm} \\
S_y &= \dfrac{-i\hbar}{2}(\ket{+}\bra{-} - \ket{-}\bra{+})
  & \ket{s_y,\pm} &= \dfrac{1}{\sqrt{2}}(\ket{+}\pm i\ket{-}) \\
S_x &= \dfrac{\hbar}{2}(\ket{+}\bra{-} + \ket{-}\bra{+})
  & \ket{s_x,\pm} &= \dfrac{1}{\sqrt{2}}(\ket{+}\pm\ket{-})
\end{align*}
\end{document}

enter image description here

I've loaded the braket package for \ket.

Alternatively, if you don't want the first equation to be aligned at the equals with the following ones, there's gather and aligned:

\documentclass[letterpaper,10pt,twocolumn,fleqn]{article}

\usepackage{amsmath,braket}

\begin{document}
\begin{gather*}
S_z\ket{\pm} = \pm\frac{\hbar}{2}\ket{\pm} \\
\!\begin{aligned}
S_{\pm} &= S_x\pm S_y \\
S_z &= \dfrac{\hbar}{2}(\ket{+}\bra{+} + \ket{-}\bra{-})
  & \ket{s_z,\pm} &= \ket{\pm} \\
S_y &= \dfrac{-i\hbar}{2}(\ket{+}\bra{-} - \ket{-}\bra{+})
  & \ket{s_y,\pm} &= \dfrac{1}{\sqrt{2}}(\ket{+}\pm i\ket{-}) \\
S_x &= \dfrac{\hbar}{2}(\ket{+}\bra{-} + \ket{-}\bra{+})
  & \ket{s_x,\pm} &= \dfrac{1}{\sqrt{2}}(\ket{+}\pm\ket{-})
\end{aligned}
\end{gather*}
\end{document}

enter image description here

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