equation out of margin?

Question

I am using

    \begin{equation}
        equation
    \end{equation} 

in order to write formulas

but for example with

\begin{equation}
G(\boldsymbol{x_1}, \overline{z} -dz/2; \boldsymbol{x_2}, \overline{z} +dz/2) = {\displaystyle\int }  \frac{d^2 \boldsymbol Q}{{2 \pi}} [\widetilde{C_0}(\boldsymbol{Q}) e^{-i Q^2 dz/2k}] e^{i \boldsymbol{Q} \cdot (\boldsymbol{x_2}-\boldsymbol{x_1})} \times  \notag\\ {\displaystyle\int }  \frac{d^2 \boldsymbol q}{{2 \pi}} [\widetilde{I_0}(\boldsymbol{q}) e^{-i q^2 dz/8k}] e^{i \boldsymbol{q} \cdot [\boldsymbol{x_2}+\boldsymbol{x_1}]/2} e^{-i \boldsymbol{Q}\cdot \boldsymbol{q}(\overline z /k)}
\end{equation}

I obtain

How can I correct it?

Answer 1

You can't break lines with \\ inside equation; you need a specific alignment environment, in this case split.

The terms at which it's possible to split are very long, so I suggest to set the left-hand side on a line by itself and indenting the right-hand side split into two lines.

The code:

\documentclass{article}
\usepackage{amsmath,bm}

\newcommand{\vect}[1]{\boldsymbol{#1}}

\begin{document}

\begin{equation}
\begin{split}
& G(\vect{x}_1, \bar{z} -dz/2; \vect{x}_2, \bar{z} +dz/2)
\\
&\qquad = \int \frac{d^2 \vect Q}{2 \pi}
               [\tilde{C}_0(\vect{Q}) e^{-i Q^2 dz/2k}]
               e^{i \vect{Q} \cdot (\vect{x}_2-\vect{x}_1)}
\\
&\qquad \times \int \frac{d^2 \vect{q}}{2 \pi}
                    [\tilde{I}_0(\vect{q}) e^{-i q^2 dz/8k}]
                    e^{i \vect{q} \cdot [\vect{x}_2+\vect{x}_1]/2}
                    e^{-i \vect{Q}\cdot \vect{q}(\bar{z}/k)}
\end{split}
\end{equation}

\end{document}

I have also other suggestions:

1. \boldsymbol{x_1} should be \boldsymbol{x}_1
2. It's better to have a more semantic command, so I defined \vect to use \boldsymbol
3. {\displaystyle\int} is wrong: just use \int.
4. Instead of \overline it's better to use \bar over single symbols.
5. Similarly for \widetilde, which need not cover the subscript, and can well be \tilde; don't worry: your readers will see it.

Answer 2

As I said, the equation is just too long. You can either use multline or align with \MoveEqLeft from mathtools. I am also a bit unsure of the notation, the d in dz is not meant to be a differential, is it? In any case, it is very helpful if the reader knows what is meant, and clearly mark differentials. Likewise, you want to have the imaginary i and the Euler e distinguishable from indices and variables. Given that I do not know the context one guess for the equation could be:

\documentclass{article}
\usepackage{mathtools}
\newcommand{\diff}{\mathop{}\!\mathrm{d}}
\begin{document}
\begin{align}
 \MoveEqLeft
G(\boldsymbol{x}_1, \overline{z} -dz/2; \boldsymbol{x_2}, \overline{z} +dz/2) 
= \int\!  \frac{\diff^2 \boldsymbol Q}{{2 \pi}} \,
\bigl[\widetilde{C_0}(\boldsymbol{Q})\, \mathrm{e}^{-\mathrm{i} Q^2 dz/2k}\bigr]\, 
\mathrm{e}^{\mathrm{i} \boldsymbol{Q} \cdot 
(\boldsymbol{x}_2-\boldsymbol{x}_1)}   \notag\\ 
&{}\times\int   \!\frac{\diff^2 \boldsymbol q}{{2 \pi}} \,
\bigl[\widetilde{I_0}(\boldsymbol{q})\, 
\mathrm{e}^{-\mathrm{i} q^2 dz/8k}\bigr]\, 
\mathrm{e}^{\mathrm{i} \boldsymbol{q} \cdot 
[\boldsymbol{x}_2+\boldsymbol{x}_1]/2}\, 
\mathrm{e}^{-\mathrm{i} \boldsymbol{Q}\cdot \boldsymbol{q}(\overline z /k)}
\;.
\end{align}
\end{document}