summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/fonts/garamond-math/Garamond-Math.tex
diff options
context:
space:
mode:
authorKarl Berry <karl@freefriends.org>2019-01-27 22:47:32 +0000
committerKarl Berry <karl@freefriends.org>2019-01-27 22:47:32 +0000
commit8e627b933f0617923284400b0b9ca2731973a690 (patch)
tree820e659a377edd2c1ac4c70abc0689cfc026c25a /Master/texmf-dist/doc/fonts/garamond-math/Garamond-Math.tex
parentc03d091e2fc911a63b0f4845467ee0a1a21c73d9 (diff)
garamond-math (27jan19)
git-svn-id: svn://tug.org/texlive/trunk@49835 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/fonts/garamond-math/Garamond-Math.tex')
-rw-r--r--Master/texmf-dist/doc/fonts/garamond-math/Garamond-Math.tex295
1 files changed, 295 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/fonts/garamond-math/Garamond-Math.tex b/Master/texmf-dist/doc/fonts/garamond-math/Garamond-Math.tex
new file mode 100644
index 00000000000..d4765579c87
--- /dev/null
+++ b/Master/texmf-dist/doc/fonts/garamond-math/Garamond-Math.tex
@@ -0,0 +1,295 @@
+\documentclass[a4paper,fleqn]{article}
+\usepackage[a4paper, margin=1in]{geometry}
+\usepackage{amsmath}
+\usepackage[math-style=ISO, bold-style=ISO]{unicode-math}
+\usepackage{metalogo}
+
+\setmathfont{Garamond-Math.otf}[Path=./]
+\setmathfont{Garamond-Math.otf}[version=GaramondMathI ,StylisticSet={1},Path=./]
+\setmathfont{Garamond-Math.otf}[version=GaramondMathII ,StylisticSet={2},Path=./]
+\setmathfont{Garamond-Math.otf}[version=GaramondMathIII ,StylisticSet={3},Path=./]
+\setmathfont{Garamond-Math.otf}[version=GaramondMathIV ,StylisticSet={4},Path=./]
+\setmathfont{Garamond-Math.otf}[version=GaramondMathV ,StylisticSet={5},Path=./]
+\setmathfont{Garamond-Math.otf}[version=GaramondMathVI ,StylisticSet={6},Path=./]
+\setmathfont{Garamond-Math.otf}[version=GaramondMathVII ,StylisticSet={7},Path=./]
+\setmathfont{Garamond-Math.otf}[version=GaramondMathVIII,StylisticSet={8},Path=./]
+\setmathfont{Garamond-Math.otf}[version=GaramondMathIX ,StylisticSet={9},Path=./]
+
+\def\Latinalphabets{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
+\def\latinalphabets{abcdefghijklmnopqrstuvwxyz}
+\def\Greekalphabets{%
+ \Alpha \Beta \Gamma \Delta \Epsilon
+ \Zeta \Eta \Theta \varTheta \Iota
+ \Kappa \Lambda \Mu \Nu \Xi
+ \Omicron \Pi \Rho \Sigma \Tau
+ \Upsilon \Phi \Chi \Psi \Omega
+}
+\def\greekalphabets{%
+ \alpha \beta \gamma \delta \epsilon
+ \zeta \eta \theta \vartheta
+ \iota \kappa \varkappa \lambda \mu
+ \nu \xi \omicron \pi \varpi \rho
+ \varrho \sigma \varsigma \tau \upsilon
+ \phi \varphi \chi \psi \omega
+}
+% ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ
+% αβγδεζηθικλμνξοπρστυφχψω
+\def\TOPACCENT#1{%
+ \acute{#1} \, \bar{#1} \, \breve{#1} \, \check{#1} \, \ddddot{#1} , \quad
+ \dddot{#1} \, \ddot{#1} \, \dot{#1} \, \grave{#1} \, \hat{#1} , \quad
+ \mathring{#1} \, \tilde{#1} \, \vec{#1} \, \widehat{#1} \, \widetilde{#1}
+}
+\ExplSyntaxOn
+\NewDocumentCommand \TOPACCENTMAP { m m }
+ { \fonttest_top_accent_map:Nx #1 {#2} }
+\cs_new:Npn \fonttest_top_accent_map:Nn #1#2
+ { \tl_map_inline:nn {#2} { \[ \TOPACCENT{#1{##1}} \] } }
+\cs_generate_variant:Nn \fonttest_top_accent_map:Nn { Nx }
+\NewDocumentCommand \SUPSUBMAP { m m }
+ { \[ \exp_args:Nx \tl_map_inline:nn {#2} {{ #1{##1 \sb{\QED}} }} \] }
+\NewDocumentCommand \CIRCLEDNUMA { s }
+ {
+ % with *: 0-50
+ % without *: 0-10
+ \symbol {"24EA}
+ \fonttest_circled_aux:nn {"2460} {"2469}
+ \IfBooleanT {#1}
+ {
+ \fonttest_circled_aux:nn {"246A} {"2473}
+ \fonttest_circled_aux:nn {"3251} {"325F}
+ \fonttest_circled_aux:nn {"32B1} {"32BF}
+ }
+ }
+\NewDocumentCommand \CIRCLEDNUMB { s }
+ {
+ % with *: 0-20
+ % without *: 0-10
+ \symbol {"24FF}
+ \fonttest_circled_aux:nn {"2776} {"277F}
+ \IfBooleanT {#1}
+ { \fonttest_circled_aux:nn {"24EB} {"24F4} }
+ }
+\NewDocumentCommand \CIRCLEDNUMC { }
+ { \fonttest_circled_aux:nn {"24F5} {"24FE} }
+\NewDocumentCommand \CIRCLEDLETTERA { }
+ { \fonttest_circled_aux:nn {"24B6} {"24CF} }
+\NewDocumentCommand \CIRCLEDLETTERB { }
+ { \fonttest_circled_aux:nn {"1F150} {"1F169} }
+\NewDocumentCommand \CIRCLEDLETTERC { }
+ { \fonttest_circled_aux:nn {"24D0} {"24E9} }
+\cs_new:Npn \fonttest_circled_aux:nn #1#2
+ { \int_step_inline:nnn {#1} {#2} { \symbol {##1} } }
+\ExplSyntaxOff
+\def\OVERUNDERLINE#1{%
+ #1{} \quad #1{b} \quad #1{ab} \quad #1{abc} \quad #1{abcd} \quad #1{abcde} \quad #1{a+b+c}}
+\def\LISTTEXT{x_1, \, x_2, \, x_3,\ x_4\, \ \ldots, \, x_n}
+
+\DeclareRobustCommand{\GenericInfo}[2]{}
+
+\def\ee{\symrm{e}}
+\def\ii{\symrm{i}}
+\def\bm{\symbf}
+\newcommand{\innerprod}[2]{\left\langle{#1}\middle\vert{#2}\right\rangle}
+\newcommand{\brakket}[3]{\left\langle{#1}\middle\vert{#2}\middle\vert{#3}\right\rangle}
+\newcommand{\ket}[1]{\left\lvert{#1}\right\rangle}
+\newcommand{\kets}[1]{\lvert{#1}\rangle}
+\newcommand{\bra}[1]{\left\langle{#1}\right\rvert}
+\newcommand{\ip}[2]{\left\langle{#1}\middle\vert{#2}\right\rangle}
+\newcommand{\op}[2]{\left\lvert{#1}\middle\rangle\middle\langle{#2}\right\rvert}
+\newcommand{\dd}{\text{d}}
+\newcommand{\norm}[1]{\left\lVert{#1}\right\rVert}
+
+\title{Garamond-Math, Ver. 0.3}
+\author{Yuansheng Zhao, Xiangdong Zeng}
+
+\begin{document}
+\maketitle
+\section{Introduction}
+Garamond-Math is an open type math font matching the \emph{EB Garamond (Octavio Pardo)}\footnote{https://ctan.org/pkg/ebgaramond/, and https://github.com/octaviopardo/EBGaramond12/} and \emph{EB Garamond (Georg Mayr-Duffner)}\footnote{https://github.com/georgd/EB-Garamond/}.
+Many mathematical symbols are derived from other fonts, others are made from scratch. The metric is generated with a python script.
+
+The font is best used with \XeTeX, with other engine, one might end up getting very bad spacing.
+
+This font is still under development, do not expect the font to be free of bugs. We might update any components any at any time. Issues, bug reports, forks and other contributions are welcome. Please visit GitHub (https://github.com/YuanshengZhao/Garamond-Math/) for development details.
+
+The minimal example with \texttt{unicode-math} package is as following:
+\begin{verbatim}
+ %Compile with XeTeX
+ \documentclass{article}
+ \usepackage[math-style=ISO, bold-style=ISO]{unicode-math}
+ \setmainfont{EB Garamond}%You should have installed the font
+ \setmathfont{Garamond-Math.otf}[StylisticSet={7,9}]%Use StylisticSet that you like
+ \begin{document}
+ \[x^3+y^3=z^3\]
+ \end{document}
+\end{verbatim}
+
+\section{Alphabets \& StylisticSet}
+The text font in this document is set to Latin Modern Roman deliberately so that the difference between text and math can be easily seen.
+\subsubsection*{Latin and Greek (StylisticSet 4/5 give semi/extra bold for \texttt{\backslash symbf})}
+Each letter is regarded as variable, so the spacing is larger than usual text. I recommend typing equations like this (pay attention to \texttt{\backslash sumup} $\ee$, $\ii$, and text $\cos$, $\dd$): $\ee^{\ii k z}=\cos k z-\ii\int_0^{kz}\cos \zeta\,\dd\zeta$.
+\[ \Latinalphabets\]
+\[ \latinalphabets \]
+\[ \symup{\Latinalphabets}\]
+\[ \symup{\latinalphabets} \]
+\[ \symbf{\Latinalphabets}\]
+\[ \symbf{\latinalphabets}\]
+\[ \symbfup{\Latinalphabets}\]
+\[ \symbfup{\latinalphabets} \]
+\[ \Greekalphabets \]
+\[\greekalphabets\]
+\[ \symup{\Greekalphabets} \]
+\[\symup{\greekalphabets} \]
+\[ \symbf{\Greekalphabets} \]
+\[\symbf{\greekalphabets} \]
+\[ \symbfup{\Greekalphabets}\]
+\[ \symbfup{\greekalphabets} \]
+\begingroup\mathversion{GaramondMathIV}\[\symbf{\Latinalphabets}\]
+\[\symbf{\latinalphabets}\]\endgroup
+\begingroup\mathversion{GaramondMathV}\[\symbf{\Latinalphabets}\]
+\[\symbf{\latinalphabets}\]\endgroup
+
+\subsubsection*{Sans and Typerwriter: From Libertinus Math\footnote{https://github.com/khaledhosny/libertinus/}}
+\[ \symsf{\Latinalphabets} \]
+\[\symsf{\latinalphabets} \]
+\[ \symsfup{\Latinalphabets} \]
+\[\symsfup{\latinalphabets} \]
+\[ \symbfsf{\Latinalphabets} \]
+\[\symbfsf{\latinalphabets} \]
+\[ \symbfsfup{\Latinalphabets} \]
+\[\symbfsfup{\latinalphabets} \]
+\[ \symtt{\Latinalphabets}\]
+\[\symtt{\latinalphabets} \]
+
+\subsubsection*{Blackboard (StylisticSet 1 gives rounded XITS Math\footnote{https://github.com/khaledhosny/xits/})}
+\[ \symbb{\Latinalphabets} \]
+\[\symbb{\latinalphabets} \]
+\begingroup\mathversion{GaramondMathI}\[\symbb{\Latinalphabets}\]
+\[\symbb{\latinalphabets}\]\endgroup
+
+\subsubsection*{Script: Rounded XITS Math [StylisticSet 3 gives scaled CM; 8 gives Garamond-compatible ones (experimental)]}
+\[ \symscr{\Latinalphabets} \]
+\[\symscr{\latinalphabets} \]
+\[ \symbfscr{\Latinalphabets} \]
+\[\symbfscr{\latinalphabets} \]
+\begingroup\mathversion{GaramondMathIII}\[\symscr{\Latinalphabets}\]
+\[\symbfscr{\Latinalphabets}\]\endgroup
+\begingroup\mathversion{GaramondMathVIII}\[\symscr{\Latinalphabets}\]
+\[\symscr{\latinalphabets}\]\endgroup
+
+\subsubsection*{Digits: Same width between weight and serif/sans}
+\[3.141592653589793238462643383279502884197169399375105820974944592307816406286\]
+\[\symsf{3.141592653589793238462643383279502884197169399375105820974944592307816406286}\]
+\[\symbf{3.141592653589793238462643383279502884197169399375105820974944592307816406286}\]
+
+\subsubsection*{\texttt{\backslash partial}: (StylisticSet 2 gives curved ones)}
+\[\partial_\mu(\symup\partial^\mu\phi)-\symbf{\epsilon^{\lambda\mu\nu}\partial_\mu(A_\lambda\symbfup\partial_\nu f)}\]
+\begingroup\mathversion{GaramondMathII}\[\partial_\mu(\symup\partial^\mu\phi)-\symbf{\epsilon^{\lambda\mu\nu}\partial_\mu(A_\lambda\symbfup\partial_\nu f)}\]\endgroup
+
+\subsubsection*{\texttt{\backslash hbar}: (StylisticSet 6 gives horizontal bars)}
+\[\text{$\hbar$\qquad \begingroup\mathversion{GaramondMathVI} $\hbar$\endgroup}\]
+
+\subsubsection*{\texttt{\backslash tilde}: (StylisticSet 9 gives ``normal'' ones)}
+\[\text{$\tilde F$\qquad \begingroup\mathversion{GaramondMathIX} $\tilde F$\endgroup}\]
+
+\subsubsection*{\texttt{\backslash int}: (StylisticSet 7 gives a variant with inversion symmetry)}
+\[\oint_{\partial\Sigma}\vec E\cdot \dd{\vec{l}}=-\frac{1}{c}\frac{\dd}{\dd t}\iint_{\Sigma}\vec B \cdot \dd{\vec{S}}\]
+\begingroup\mathversion{GaramondMathVII}\[\oint_{\partial\Sigma}\vec E\cdot \dd{\vec{l}}=-\frac{1}{c}\frac{\dd}{\dd t}\iint_{\Sigma}\vec B \cdot \dd{\vec{S}}\]\endgroup
+
+\section{Known Issue}
+\begin{itemize}
+ \item As mentioned before, the font should only be used with \XeTeX.
+ \item Various spacing problems. Though math fonts technically should not be kerned, some pairs looks very ugly (Ex. $VA$); sometimes sub/superscript may also have same problem.
+ \item Fake optical size. EB Garamond does not contain a complete set of glyphs (normal + bold + optical size of both weights). The ``optical size \texttt{ssty}'' is made by interpolating different weights at the present (without this, the double script is too thin to be readable).
+\end{itemize}
+
+\section{Equation Samples}
+\[ 1 + 2 - 3 \times 4 \div 5 \pm 6 \mp 7 \dotplus 8 = -a \oplus b \otimes c -\{z\}\]
+\[\forall \epsilon, \exists \delta : x \in A \cup B \subset S \cap T \ntrianglerighteq U\]
+\[R_{\nu\kappa\lambda}^\mu=\partial_\kappa\Gamma_{\lambda\nu}^\mu-\partial_\lambda\Gamma_{\kappa\nu}^\mu+\Gamma_{\kappa\sigma}^\mu\Gamma_\lambda\nu^\sigma-\Gamma_{\lambda\sigma}^\mu\Gamma_{\kappa\nu}^\sigma\]
+\[T_{\alpha_1,\cdots\alpha_k}'^{\beta_1\cdots\beta_l}=T_{i_1\cdots i_k}^{j_1\cdots j_l}
+ \frac{\partial x^{i_1}}{\partial x'^{\alpha_1}}\cdots
+ \frac{\partial x^{i_k}}{\partial x'^{\alpha_k}}
+ \frac{\partial x'^{\beta_1}}{\partial x^{j_1}}\cdots
+ \frac{\partial x'^{\beta_l}}{\partial x^{j_l}}
+\]
+\[\int_{\sqrt{\frac{1-m u+m\Delta/k^2}{2mu/k}}}^{X_p}\widehat{1+2+3+4}+\widetilde{5+6+7+8}\]
+\[ x \leftarrow y \leftrightarrow w \Rightarrow b \Leftrightarrow c
+ \uparrow y \updownarrow w \Downarrow b \Updownarrow c
+ \Searrow p \Swarrow p
+ x \leftharpoonup x \upharpoonleft
+ X \mapsfrom Y \mapsto Z \mapsup
+ f \rightleftarrows f \updownarrows f
+ h \rightthreearrows h \leftthreearrows
+ p
+\]
+\[\int_0^1\frac{\ln (x+1)}{x}\dd{x}=\int_0^1\sum_{i=1}^{\infty}\frac{(-x)^{i-1}}{i}\dd{x}=\sum_{i=1}^{\infty}\int_0^1\frac{(-x)^{i-1}}{i}\dd{x}=\sum_{i=1}^{\infty}\frac{(-1)^{i+1}}{i^2}=\frac{\uppi^2}{12}\]
+\[
+ \int\limits_0^\infty \int_0^\infty
+ \sum_{i=1}^\infty \prod_{j=i}^\infty \coprod_{k=i}^\infty
+ \oiiint \varointclockwise \ointctrclockwise \awint \intclockwise
+\]
+\[
+ \Biggl( \biggl( \Bigl( \bigl( (x) \bigr) \Bigr) \biggr) \Biggr) \quad
+ \Biggl[ \biggl[ \Bigl[ \bigl[ [x] \bigr] \Bigr] \biggr] \Biggr] \quad
+ \Biggl\{ \biggl\{ \Bigl\{ \bigl\{ \{x\} \bigr\} \Bigr\} \biggr\} \Biggr\}\quad
+ \Biggl\lvert \biggl\lvert \Bigl\lvert \bigl\lvert \lvert x\rvert \bigr\rvert \Bigr\rvert\biggr\rvert \Biggr\rvert\quad
+ \Biggl\lVert \biggl\lVert \Bigl\lVert \bigl\lVert \lVert x\rVert \bigr\rVert \Bigr\rVert\biggr\rVert \Biggr\rVert\quad
+ \Biggl\langle \biggl\langle \Bigl\langle \bigl\langle \langle x\rangle \bigr\rangle \Bigr\rangle\biggr\rangle \Biggr\rangle\quad
+\]
+\[
+ \Biggl\lgroup \biggl\lgroup \Bigl\lgroup \bigl\lgroup \lgroup x\rgroup \bigr\rgroup \Bigr\rgroup\biggr\rgroup \Biggr\rgroup\quad
+\Biggl\lfloor \biggl\lfloor \Bigl\lfloor \bigl\lfloor \lfloor x\rfloor \bigr\rfloor \Bigr\rfloor\biggr\rfloor \Biggr\rfloor\quad
+\Biggl\lceil \biggl\lceil \Bigl\lceil \bigl\lceil \lceil x\rceil \bigr\rceil \Bigr\rceil\biggr\rceil \Biggr\rceil\quad\]
+\[
+ \bra{x} + \ket{x} + \ip{\alpha}{\beta} + \op{\alpha}{\beta}
+ + \bra{\frac{1}{2}} + \ket{\frac{1}{2}}
+ + \ip{\frac{1}{2}}{\frac{1}{2}} + \op{\frac{1}{2}}{\frac{1}{2}}
+ + \bra{\frac{a^2}{b^2}}
+ + \Biggl\vert \frac{\mathrm{e}^{x^2}}{\mathrm{e}^{y^2}} \Biggr\rangle
+\]
+\[
+ \CIRCLEDNUMB +
+ ABC^{\CIRCLEDNUMA}
+\]
+\[\left( \begin{matrix}
+{{u}_{0}} \\
+{{u}_{1}} \\
+\vdots \\
+{{u}_{N-1}} \\
+\end{matrix} \right)=\sum\limits_{k>0}{\left[ \left( \begin{matrix}
+ 1 \\
+ \cos ka \\
+ \vdots \\
+ \cos k\left( N-1 \right)a \\
+ \end{matrix} \right)\underbrace{{{C}_{k+}}\cos ( {{\omega }_{k}}t+{{\varphi }_{k+}} )}_{\frac{2}{\sqrt{N}}{{q}_{k+}}}+\left( \begin{matrix}
+ 0 \\
+ \sin ka \\
+ \vdots \\
+ \sin k\left( N-1 \right)a \\
+ \end{matrix} \right)\underbrace{{{C}_{k-}}\cos ( {{\omega }_{k}}t+{{\varphi }_{k-}} )}_{\frac{2}{\sqrt{N}}{{q}_{k-}}} \right]}\]
+\[
+\begin{split}
+\mathcal{F}^{-1}(\kets{j})
+&{}=\frac{1}{\sqrt{2^n}}\sum_{k=0}^{2^n-1}\exp\left(-2\uppi \ii \frac{jk}{2^n}\right)\kets{k}.\\
+&{}=\frac{1}{\sqrt{2^n}}\sum_{k_{n-1}=0}^1\cdots\sum_{k_{0}=0}^1\exp\left(-2\uppi \ii j\sum_{l=0}^{n-1}\frac{2^l k_l}{2^n}\right)\kets{k_{n-1}\cdots k_0}\\
+&{}=\frac{1}{\sqrt{2^n}}\sum_{k_{n-1}=0}^1\cdots\sum_{k_{0}=0}^1\bigotimes_{l=1}^n\left[\exp\left(-2\uppi \ii j\frac{k_{n-l}}{2^l}\right)\kets{k_{n-l}}\right]\\
+&{}=\frac{1}{\sqrt{2^n}}\bigotimes_{l=1}^n\left[\sum_{k_{n-l}=0}^1\exp\left(-2\uppi \ii j\frac{k_{n-l}}{2^l}\right)\kets{k_{n-l}}\right]\\
+&{}=\frac{1}{\sqrt{2^n}}\bigotimes_{l=1}^n\left[\kets{0}_{n-l}+\ee^{-2\uppi \ii j /2^l}\kets{1}_{n-l}\right]\\
+&{}=\frac{1}{\sqrt{2^n}}\bigotimes_{l=1}^n\left[\kets{0}_{n-l}+\ee^{-2\uppi \ii ({0.j_{l-1}\ldots j_0})}\kets{1}_{n-l}\right].
+\end{split}
+\]
+
+\newcommand{\lb}{\left(}
+\newcommand{\rb}{\right)}
+\newcommand{\piup}{\uppi}
+\newcommand{\ndd}{\,\mathrm{d}}
+\[\begin{split}S&{}=\frac{m}{2}\int_0^{t_{\text f}}\left[\lb-\omega x_{\text i}\sin\omega t+\omega \frac{x_{\text f}-x_{\text i}\cos\omega t_{\text f}}{\sin\omega t_{\text f}}\cos\omega t\rb^2+\sum_{n=1}^\infty\lb\frac{a_n n \piup}{t_{\text f}}\rb^2\cos^2\frac{n \piup t}{t_{\text f}}\right]\ndd t\\%
+ &\quad{}-\frac{m\omega^2}{2}\int_0^{t_{\text f}}\left[\lb x_{\text i}\cos\omega t+ \frac{x_{\text f}-x_{\text i}\cos\omega t_{\text f}}{\sin\omega t_{\text f}}\sin\omega t\rb^2+\sum_{n=1}^\infty {a_n}^2\sin^2\frac{n \piup t}{t_{\text f}}\right]\ndd t\\%
+ &{}=\sum_{n=1}^\infty\int_0^{t_{\text f}}\left[\frac{m}{2}\lb\frac{a_n n \piup}{t_{\text f}}\rb^2\cos^2\frac{n \piup t}{t_{\text f}}-\frac{m\omega^2}{2}{a_n}^2\sin^2\frac{n \piup t}{t_{\text f}}\right]\ndd t\\%
+ &\quad{}+\frac{m\omega^2}{2}\int_0^{t_{\text f}}\left[ {x_{\text i}}^2-\lb\frac{x_{\text f}-x_{\text i}\cos\omega t_{\text f}}{\sin\omega t_{\text f}}\rb^2\right]\lb\sin^2\omega t-\cos^2\omega t\rb\ndd t\\%
+ &\quad{}-\frac{m\omega^2}{2}\int_0^{t_{\text f}}4 {x_{\text i}}\lb\frac{x_{\text f}-x_{\text i}\cos\omega t_{\text f}}{\sin\omega t_{\text f}}\rb\lb\sin\omega t\cos\omega t\rb\ndd t.\end{split}\]
+ \[\begin{split}U\lb x_{\text f},t_{\text f};x_{\text i},t_{\text i}\rb=&\sqrt{\frac{m\omega}{2\piup \ii \hbar\sin\left[\omega\lb t_{\text f}-t_{\text i}\rb\right]}}\\&{}\times\exp\left\{\frac{\ii m\omega}{2\hbar\sin\left[\omega \lb t_{\text f}-t_{\text i}\rb\right]}\left[\lb {x_{\text i}}^2+{x_{\text f}}^2\rb\cos\left[\omega\lb t_{\text f}-t_{\text i}\rb\right]-2 x_{\text i} x_{\text f}\right]\right\}.\end{split}\]
+\end{document}
+
+