为什么我的方程式*环境中出现“缺少 $ 插入错误”

Question

代码如下：

\begin{equation*}
\[I(t)=\begin{cases}
1; & |t|\le\frac{{\Delta}t_{p}^{FWHM}}{2}\\
0; & |t|>\frac{{\Delta}t_{p}^{FWHM}}{2}
\end{cases}\]
 \end{equation*}\\

错误是缺少插入的 $ 和错误的数学分隔符，我该怎么办？

我尝试生成一个表格，上面的代码是表格中的一些公式，完整代码如下：

\begin{table}[!htb]
\begin{center}
\renewcommand{\arraystretch}{2.7}
\begin{tabular}{|c|c|}
\hline
\multicolumn{2}{|c|}{Square Pulse} \\
\hline
Pulse & 
\begin{equation*}
\[I(t)=\begin{cases}
1; & |t|\le\frac{{\Delta}t_{p}^{FWHM}}{2}\\
0; & |t|>\frac{{\Delta}t_{p}^{FWHM}}{2}
\end{cases}\]
 \end{equation*}\\
 \hline
Autocorrelation & 
\begin{equation*}
    \[A^{(2)}(\tau)=\begin{cases}1-|\frac{\tau}{\Delta\tau_{A}^{FWHM}}|; &|\tau|\le\Delta\tau_{A}^{FWHM}\\
0; &|\tau|>\Delta\tau_{A}^{FWHM}\end{cases}\]
\end{equation*} \\
 \hline
 Relationship & ${\Delta}t_{p}^{FWHM}=\Delta\tau_{A}^{FWHM}$ \\
 \hline
 \multicolumn{2}{|c|}{Gaussian Pulse} \\
 \hline
 Pulse & $I(t)=exp[-(2\sqrt{ln2t}/{\Delta}t_{p}^{FWHM})^2]$ \\ 
 \hline
 Autocorrelation & $A^{(2)}(\tau)=exp[-         (2\sqrt{ln2\tau}}/{\Delta\tau_{A}^{FWHM}})^2)^2$ \\
 \hline
 Relationship & $1.41{\Delta}t_{p}^{FWHM}=\Delta\tau_{A}^{FWHM}$ \\
 \hline
 \end{tabular}
\centering{
\caption{The relationship between the initial pulse and autocorrelation of square pulse and Gaussian pulse}
\label{table AC1}}
\end{center}
\end{table}

Answer 1

你不应该使用\begin{equation*} ... \end{equation*} 或者 \[ ... \]在环境的列内tabular。相反，只需将右侧列的列定义从 更改为c即可>{$\displaystyle}c<{$}；这将确保第二列中的所有单元格都自动处于数学模式。

您的等式中存在多个（语法）错误。另外，请写成\expand\ln而不是expand ln；这样，“exp”和“ln”将使用直立字母排版。

此外，如果可能的话，避免在第二列中使用分数表达式\frac；而是使用“内联样式”分数，例如，a/b而不是\frac{a}{b}。

\documentclass{article}
\usepackage{mathtools,array}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\newcommand\FWHM{\mathrm{FWHM}}
\begin{document}
\begin{table}[!htb]
\centering
\renewcommand{\arraystretch}{2.75}
\begin{tabular}{|l|>{$\displaystyle}l<{$}|}
\hline
\multicolumn{2}{|c|}{Square Pulse} \\
\hline
Pulse & 
I(t)=
\begin{cases}
1; & \abs{t}\le\tfrac{1}{2}\Delta t_{p}^{\FWHM}\\[1.5ex]
0; & \abs{t}>  \tfrac{1}{2}\Delta t_{p}^{\FWHM}
\end{cases}
 \\
\hline
Autocorrelation & 
A^{(2)}(\tau)=
\begin{cases}
1-\abs*{\tau\big/\Delta\tau_{A}^{\FWHM}}; 
& \abs{\tau}\le\Delta\tau_{A}^{\FWHM}\\[2ex]
0;  & \abs{\tau}>\Delta\tau_{A}^{\FWHM}
\end{cases}
 \\
\hline
Relationship & {\Delta}t_{p}^{\FWHM}=\Delta\tau_{A}^{\FWHM} \\
\hline
 \multicolumn{2}{|c|}{Gaussian Pulse} \\
 \hline
 Pulse & I(t)=\exp\Bigl[-\bigl(2\sqrt{\ln2t}/{\Delta}t_{p}^{\FWHM}\bigr)^2\Bigr] \\ 
\hline
Autocorrelation & 
A^{(2)}(\tau)=\exp\Bigl[-\bigl(2\sqrt{\ln2\tau}/\Delta\tau_{A}^{\FWHM}\bigr)^2\Bigr] \\
\hline
Relationship & 
{\Delta}t_{p}^{\FWHM}=\Delta\tau_{A}^{\FWHM} \\
\hline
 \end{tabular}
\caption{The relationship between the initial pulse and autocorrelation of square pulse and Gaussian pulse}
\label{table AC1}
\end{table}

\end{document}

---

附录：您的表格包含许多垂直线和水平线，这实际上并没有提高其内容的可读性。您可能需要考虑让表格看起来更“开放”，例如，删除所有垂直线和大多数水平线。我希望您会同意，下表对读者的眼睛（和大脑）来说更“吸引人”……

\documentclass{article}
\usepackage{mathtools,array,booktabs}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}  % "absolute value" macro
\newcommand\FWHM{\mathrm{FWHM}}
\begin{document}
\begin{table}[!htb]
\centering
\renewcommand{\arraystretch}{1.25}
\begin{tabular}{@{}l>{$\displaystyle}l<{$}@{}}
\toprule
\multicolumn{2}{@{}l}{\bfseries Square Pulse} \\
\addlinespace
Pulse & 
I(t)=
\begin{cases}
1; & \abs{t}\le\tfrac{1}{2}\Delta t_{p}^{\FWHM}\\[1ex]
0; & \abs{t}>  \tfrac{1}{2}\Delta t_{p}^{\FWHM}
\end{cases}
 \\
\addlinespace
Autocorrelation & 
A^{(2)}(\tau)=
\begin{cases}
1-\abs*{\tau\big/\Delta\tau_{A}^{\FWHM}}; 
& \abs{\tau}\le\Delta\tau_{A}^{\FWHM}\\[1ex]
0;  & \abs{\tau}>\Delta\tau_{A}^{\FWHM}
\end{cases}
 \\
\addlinespace
Relationship & {\Delta}t_{p}^{\FWHM}=\Delta\tau_{A}^{\FWHM} \\
\midrule
\multicolumn{2}{@{}l}{\bfseries Gaussian Pulse} \\
\addlinespace
Pulse & I(t)=\exp\bigl[-\bigl(2\sqrt{\ln2t}\big/{\Delta}t_{p}^{\FWHM}\bigr)^2\,\bigr] \\ 
\addlinespace
Autocorrelation & 
A^{(2)}(\tau)=\exp\bigl[-\bigl(2\sqrt{\ln2\tau}\big/\Delta\tau_{A}^{\FWHM}\bigr)^2\,\bigr] \\
\addlinespace
Relationship & 
{\Delta}t_{p}^{\FWHM}=\Delta\tau_{A}^{\FWHM} \\
\bottomrule
 \end{tabular}
\caption{Relationship between initial pulse and autocorrelation for square and Gaussian pulses}
\label{table AC1}
\end{table}

\end{document}