忽略通用前导码，我找不到导致错误的原因？

Question

\documentclass{article}
\usepackage{biblatex}
\usepackage{amsmath,amssymb}
\usepackage{graphicx}
\usepackage{physics}
\usepackage{color}
\usepackage[export]{adjustbox}
\usepackage{subcaption}
\usepackage{mathtools}

\makeatletter
\newcommand{\Spvek}[2][r]{%
  \gdef\@VORNE{1}
  \left(\hskip-\arraycolsep%
    \begin{array}{#1}\vekSp@lten{#2}\end{array}%
  \hskip-\arraycolsep\right)}

\def\vekSp@lten#1{\xvekSp@lten#1;vekL@stLine;}
\def\vekL@stLine{vekL@stLine}
\def\xvekSp@lten#1;{\def\temp{#1}%
  \ifx\temp\vekL@stLine
  \else
    \ifnum\@VORNE=1\gdef\@VORNE{0}
    \else\@arraycr\fi%
    #1%
    \expandafter\xvekSp@lten
  \fi}
\makeatother


\begin{document}
\begin{equation}
\begin{aligned}
& \psi_1,\psi_2,\phi_1,\phi_2 \\
& \therefore \psi^*_1(\textbf{x},t)\psi_2(\textbf{x},t)e^i\phi_2(\textbf{x},t)e^-i\phi^*_1(\textbf{x},t) + \psi_1(\textbf{x},t)\psi^*_2(\textbf{x},t)e^i\phi_1(\textbf{x},t)e^-i\phi^*_2(\textbf{x},t) 
& =\psi^_1(\textbf{x},t)\psi_2(\textbf{x},t)\cos{\phi_1-\phi_2}
\end{aligned}
\end{equation}
\end{document}

我得到的错误是：

! Missing { inserted.
<to be read again> 
                   _
l.36 & =\psi^_
              1(\textbf{x},t)\psi_2(\textbf{x},t)\cos{\phi_1-\phi_2}
? 

Answer 1

似乎缺少了*一个\psi^_1。

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{physics}

\begin{document}
\begin{equation}
\begin{aligned}
& \psi_1,\psi_2,\phi_1,\phi_2 \\
& \therefore \psi^*_1(\textbf{x},t)\psi_2(\textbf{x},t)e^i\phi_2(\textbf{x},t)e^-i\phi^*_1(\textbf{x},t) + \psi_1(\textbf{x},t)\psi^*_2(\textbf{x},t)e^i\phi_1(\textbf{x},t)e^-i\phi^*_2(\textbf{x},t)\\ 
& =\psi^*_1(\textbf{x},t)\psi_2(\textbf{x},t)\cos{\phi_1-\phi_2}
\end{aligned}
\end{equation}
\end{document}