equations.tex

\documentclass[a4paper,12pt]{book}
\usepackage{amsmath}
\begin{document}
How to write complex equations in LaTeX.
\begin{equation}
	\sigma_{t}^{2}=\sigma_{Landau}^{2}+\sigma_{jitter}^{2}+\sigma_{timewalk}^{2}
\end{equation}
\begin{equation}
\sigma_{jitter}=\frac{N}{dV/dt}=\frac{t_{rise}}{(S/N)}
\end{equation}
\begin{equation}
\sigma_{timewalk}=\Big[\frac{V_{th}}{S/t_{rise}}\Big]_{RMS}\propto\Big[\frac{N}{dV/dt}\Big]_{RMS}
\end{equation}
Write functions
\begin{equation}
\sum_{i}^{} V_{ij}^{*}V_{ik}= \left\{
\begin{array}{ll}
0 & \quad if (j\neq k) \\
1 & \quad if (j = k)
\end{array}
\right.
\end{equation}
Now the decay amplitude is:
\begin{equation}
\begin{split}
< BC|H|A> & =<0|\int d^{3}r_{a}d^{3}r_{\bar{a}}d^{3}r_{b}d^{3}r_{\bar{b}}d^{3}r_{c}d^{3}r_{\bar{c}}d^{3}R\\
& e^{-iP_{B}.\Big(\frac{m_{q}r_{b}+m_{\bar{c}}r_{\bar{b}}}{m_{q}+m_{\bar{b}}}\Big)}\psi^{*}_{B(r_{b}-r_{\bar{b}})}e^{-iP_{c}.\Big(\frac{m_{c}r_{c}+m_{\bar{q}}r_{\bar{c}}}{m_{c}+m_{\bar{q}}}\Big)}\psi^{*}_{c(r_{c}-r_{\bar{c}})}\nabla|0> 
\end{split}
\end{equation}
$\overleftrightarrow{\nabla}$

\date{\today}
\begin{equation}
R_{p_{T}}=\frac{\sum_{p_{T}}^{trk}(PV_{0})}{p_{T}^{jet}}
\end{equation}
\end{document}