Align multiple equations

Question

I would like to align multiple equations below each other. However, I cannot figure out how I should code this. I'm using the following preamble:

\documentclass[11pt]{article}


%comments
%pdflatex, bibtex, pdflatex, pdflatex

\usepackage{titling}
    \setlength{\droptitle}{-12cm}

\usepackage{graphics, float}
\usepackage[pdftex]{graphicx}
\usepackage{caption}
    \usepackage{subcaption}

\usepackage{siunitx}   %allows SI units by using \SI{unit} 
\usepackage{amsmath}   %allows \begin{equation} \end{equation}

\usepackage{geometry}
\usepackage{changepage}     %allows you to widen or shorten the page width from the left or the right.

For F_{hkl} I would like to align the equations below. The equal sign of the second equation should be placed right below the equal sign in the first equation. Can someone help me figuring this out?

I am now using the following code, but I am not satisfied with it yet.

\begin{equation*}
\mathrm{F_{hkl}} = \mathrm{f_{j}} 
( \operatorname{e} ^ {2\pi \cdot i (h\cdot0 + k\cdot0 + l\cdot0)} + 
\operatorname{e} ^ {2\pi  i (h\cdot\frac{1}{2} + k\cdot\frac{1}{2} + l\cdot0)} + 
\operatorname{e} ^ {2\pi  i (h\cdot0 + k\cdot\frac{1}{2} + l\cdot\frac{1}{2})} + 
\operatorname{e} ^ {2\pi  i (h\cdot\frac{1}{2} + k\cdot0 + l\cdot\frac{1}{2})} )
\end{equation*}

\begin{equation*}
\mathrm{F_{hkl}} = \mathrm{f_{j}} 
( \operatorname{e} ^ {2\pi i \cdot 0} + 
\operatorname{e} ^ {2\pi  i (h\cdot\frac{1}{2} + k\cdot\frac{1}{2} } + 
\operatorname{e} ^ {2\pi  i (k\cdot\frac{1}{2} + l\cdot\frac{1}{2})} + 
\operatorname{e} ^ {2\pi  i (h\cdot\frac{1}{2} + l\cdot\frac{1}{2})} )
\end{equation*}

Answer 1

This type of alignment is provided out-of-the-box using amsmath's align environment:

\documentclass{article}

\usepackage{amsmath}
\newcommand{\ee}{\mathrm{e}}

\begin{document}

\[
  \mathrm{F_{hkl}} = \mathrm{f_{j}} 
  ( \ee ^ {2\pi \cdot i (h\cdot0 + k\cdot0 + l\cdot0)} + 
  \ee ^ {2\pi  i (h\cdot\frac{1}{2} + k\cdot\frac{1}{2} + l\cdot0)} + 
  \ee ^ {2\pi  i (h\cdot0 + k\cdot\frac{1}{2} + l\cdot\frac{1}{2})} + 
  \ee ^ {2\pi  i (h\cdot\frac{1}{2} + k\cdot0 + l\cdot\frac{1}{2})} )
\]

\[
  \mathrm{F_{hkl}} = \mathrm{f_{j}} 
  ( \ee ^ {2\pi i \cdot 0} + 
  \ee ^ {2\pi  i (h\cdot\frac{1}{2} + k\cdot\frac{1}{2} } + 
  \ee ^ {2\pi  i (k\cdot\frac{1}{2} + l\cdot\frac{1}{2})} + 
  \ee ^ {2\pi  i (h\cdot\frac{1}{2} + l\cdot\frac{1}{2})} )
\]

\begin{align*}
  \mathrm{F_{hkl}} &= \mathrm{f_{j}} 
  ( \ee ^ {2\pi \cdot i (h\cdot0 + k\cdot0 + l\cdot0)} + 
  \ee ^ {2\pi  i (h\cdot\frac{1}{2} + k\cdot\frac{1}{2} + l\cdot0)} + 
  \ee ^ {2\pi  i (h\cdot0 + k\cdot\frac{1}{2} + l\cdot\frac{1}{2})} + 
  \ee ^ {2\pi  i (h\cdot\frac{1}{2} + k\cdot0 + l\cdot\frac{1}{2})} ) \\
  \mathrm{F_{hkl}} &= \mathrm{f_{j}} 
  ( \ee ^ {2\pi i \cdot 0} + 
  \ee ^ {2\pi  i (h\cdot\frac{1}{2} + k\cdot\frac{1}{2} } + 
  \ee ^ {2\pi  i (k\cdot\frac{1}{2} + l\cdot\frac{1}{2})} + 
  \ee ^ {2\pi  i (h\cdot\frac{1}{2} + l\cdot\frac{1}{2})} )
\end{align*}

\end{document}

Alignments are ensured using &=.

Answer 2

In addition to using an align* environment to align the two equations on their = symbols, you may want to look into using the mathastext package to save yourself from having to type lots and lots of \mathrm "wrapper" statements.

\documentclass[11pt]{article}
\usepackage{amsmath} 
\usepackage{geometry}
\usepackage{mathastext}
\begin{document}

\begin{align*}
F_{hkl} &= f_{j} \bigl(
e ^ {2\pi \cdot i (h\cdot0 + k\cdot0 + l\cdot0)} + 
e ^ {2\pi  i (h\cdot\frac{1}{2} + k\cdot\frac{1}{2} + l\cdot0)} + 
e ^ {2\pi  i (h\cdot0 + k\cdot\frac{1}{2} + l\cdot\frac{1}{2})} + 
e ^ {2\pi  i (h\cdot\frac{1}{2} + k\cdot0 + l\cdot\frac{1}{2})} \bigr)\\
F_{hkl} &= f_{j} \bigl(
e ^ {2\pi i \cdot 0} + 
e ^ {2\pi  i (h\cdot\frac{1}{2} + k\cdot\frac{1}{2} } + 
e ^ {2\pi  i (k\cdot\frac{1}{2} + l\cdot\frac{1}{2})} + 
e ^ {2\pi  i (h\cdot\frac{1}{2} + l\cdot\frac{1}{2})} \bigr)
\end{align*}
\end{document}