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

\begin{document} 

\begin{align}
\mel{Q,t}{\rho_{S}(t)}{Q',t}&=
Tr_{B}\mel{Q,X,t}{\rho_{SB}(t)}{Q',X',t}\\ 
\begin{split} 
&=\int \underbrace{dQ_0\;dQ_0'}_{\text{initial system state differentials}}\;\underbrace{dX_0\;dX_0'}_{\text{initial bath state diferentials}}\;\underbrace{dX}_{\text{final bath state differential}}\times \\ 
& \underbrace{\mel{Q,X,t}{T \qty[e^{-\frac{i}{\hbar}\int_{0}^t H(\tau) d\tau}]}{Q_0,X_0,0}}_{\text{ right propagator}}\underbrace{\mel{Q_0',X_0',0}{T\qty[ e^{\frac{i}{\hbar}\int_{0}^t H(\tau) d\tau}]}{Q',X,t}}_{\text{left propagator}} \times\\ &\underbrace{\mel{Q_0,X_0,0}{\rho_{SB}(0)}{Q_0',X_0',0}}_{\text{initial state density matrix element}}
\end{split}
\end{align}

\end{document}

snapshot

As you can see, the label of the split environment is not centered. How to fix this?

  • 2
    Of course it is not centered, you formula extends the right margin and thus the eq no is moved out of the way. Rewrite your formula in a way that keeps the formula within the margins and it will be vertically centered – daleif Jul 9 '18 at 6:14
3

Your three-lines equation can't possibly fit within margins, unless perhaps you load geometry to have more sensible margins (if you don't use margin notes), so I propose to write it on four lines. Further I'd change a bit the layout with the fleqn environment from nccmath, and I defined a \mymel command, which is the same as \mel with better horizontal spacing and variable size delimiters, with \DeclarePairedDelimiterX from the mathtools package:

\documentclass{article}
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.3pt}
\usepackage{mathtools, nccmath, amssymb, physics}%
\DeclarePairedDelimiterX\mymel[3]{\langle}{\rangle}%
{#1\,\delimsize\vert\,\mathopen{}#2\,\delimsize\vert\,\mathopen{}#3}
\usepackage[usestackEOL]{stackengine}

\begin{document}
\begin{fleqn}
\begin{align}
\mymel{Q,t}{\rho_{S}(t)}{Q',t} & =
\Tr_{B}\mymel{Q,X,t}{\rho_{SB}(t)}{Q',X',t}\\
\begin{split}
&=\int \hspace{-1em}\underbrace{dQ_0\;dQ_0'}_{\scriptsize\Shortstack{initial system state\\ differentials}}\;\underbrace{dX_0\;dX_0'}_{\scriptsize\Shortstack{initial bath state\\ differentials}}\;\underbrace{dX_{\vphantom{0}}^{\vphantom{'}}}_{\scriptsize\Shortstack{final bath state\\ differential}}\hspace{-1.75em}\times \\
&\hphantom{{}\times{}} \underbrace{\mymel*{Q,X,t}{T \qty[e^{-\frac{i}{\hbar}\int_{0}^t H(\tau) d\tau}]}{Q_0,X_0,0}}_{\text{ right propagator}} \times \\
 &\hphantom{{}\times{}} \underbrace{\mymel*{Q_0',X_0',0}{T\qty[ e^{\frac{i}{\hbar}\int_{0}^t H(\tau) d\tau}]}{Q',X,t}}_{\text{left propagator}} \times\\
  &\hphantom{{}\times{}} \underbrace{\mymel{Q_0,X_0,0}{\rho_{SB}(0)}{Q_0',X_0',0}}_{\text{initial state density matrix element}}
\end{split}
\end{align}
\end{fleqn}

\end{document}

enter image description here

  • This looks good! I wanted to fit the "left propagator" and "right propagator" labeled factors in one line. I do understand that margin issue is unavoidable in that case. – Subho Jul 9 '18 at 10:52
1

Not totally understand your requirement, here I provide a suggestive solution.

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

\begin{document} 

\begin{align}
\mel{Q,t}{\rho_{S}(t)}{Q',t}
    &= Tr_{B}\mel{Q,X,t}{\rho_{SB}(t)}{Q',X',t} \\ 
    &= \int \underbrace{dQ_0\;dQ_0'}_{\text{initial system state differentials}}\;
            \underbrace{dX_0\;dX_0'}_{\text{initial bath state diferentials}}\;
            \underbrace{dX}_{\text{final bath state differential}}\times \notag\\ 
    &\mathrel{\phantom{=}} 
     \underbrace{\mel{Q,X,t}{T \qty[e^{-\frac{i}{\hbar}\int_{0}^t H(\tau) d\tau}]}{Q_0,X_0,0}}_{\text{ right propagator}}
      \underbrace{\mel{Q_0',X_0',0}{T\qty[ e^{\frac{i}{\hbar}\int_{0}^t H(\tau) d\tau}]}{Q',X,t}}_{\text{left propagator}} \times \notag\\
    &\mathrel{\phantom{=}} 
     \underbrace{\mel{Q_0,X_0,0}{\rho_{SB}(0)}{Q_0',X_0',0}}_{\text{initial state density matrix element}}
\end{align}

\end{document}

Output: output of solution, where lines are aligned at equal sign

Explanation:

  1. \begin{align} ... &= ... \\ ... &= ... \end{align} aligns lines at equal sign
  2. For long expression which spreads several lines, to achieve the right alignment, a phantom equal sign (occupies the width of equal sign, but typesets nothing) with math type "relation" (\mathrel{\phantom{=}}) is added before lines without a true equal sign. Note that by default the \phantom{...} is in math type "ordinary", which has different beginning and following auto-added spacing from math type "relation", the type an "normal" equal sign belongs to.
  3. For long expression which spreads several lines, to achieve the right tag (a logical line of expressions often has one tag only, no matter how many paper-lines it spreads), some \notag commands are added.

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