\documentclass[a4paper,fleqn]{article} \usepackage[a4paper, margin=1in]{geometry} \usepackage{amsmath} \usepackage[math-style=ISO, bold-style=ISO]{unicode-math} \usepackage{metalogo} \usepackage{extarrows} \makeatletter \renewcommand{\relbar}{\symbol{"E010}\mkern-.2mu\symbol{"E010}\mkern1.8mu} \renewcommand{\Relbar}{\symbol{"E011}\mkern-.2mu\symbol{"E011}\mkern1.8mu} \makeatother % \setmainfont{EB Garamond} \setmainfont{EB Garamond} % \setmonofont{Source Code Pro}[Scale=.86] \setmathfont{Garamond-Math.otf}[Path=../Release/ ]%, Scale=MatchUppercase] \setmathfont{Garamond-Math.otf}[version=GaramondMathI ,StylisticSet={1 },Path=../Release/ ]%, Scale=MatchUppercase] \setmathfont{Garamond-Math.otf}[version=GaramondMathII ,StylisticSet={2 },Path=../Release/ ]%, Scale=MatchUppercase] \setmathfont{Garamond-Math.otf}[version=GaramondMathIII ,StylisticSet={3 },Path=../Release/ ]%, Scale=MatchUppercase] \setmathfont{Garamond-Math.otf}[version=GaramondMathIV ,StylisticSet={4 },Path=../Release/ ]%, Scale=MatchUppercase] \setmathfont{Garamond-Math.otf}[version=GaramondMathV ,StylisticSet={5 },Path=../Release/ ]%, Scale=MatchUppercase] \setmathfont{Garamond-Math.otf}[version=GaramondMathVI ,StylisticSet={6 },Path=../Release/ ]%, Scale=MatchUppercase] \setmathfont{Garamond-Math.otf}[version=GaramondMathVII ,StylisticSet={7 },Path=../Release/ ]%, Scale=MatchUppercase] \setmathfont{Garamond-Math.otf}[version=GaramondMathVIII,StylisticSet={8 },Path=../Release/ ]%, Scale=MatchUppercase] \setmathfont{Garamond-Math.otf}[version=GaramondMathIX ,StylisticSet={9 },Path=../Release/ ]%, Scale=MatchUppercase] \setmathfont{Garamond-Math.otf}[version=GaramondMathX ,StylisticSet={10},Path=../Release/ ]%, Scale=MatchUppercase] \setmathfont{Garamond-Math.otf}[version=GaramondMathXI ,StylisticSet={11},Path=../Release/ ]%, Scale=MatchUppercase] \newfontfamily\GaramondMath{Garamond-Math.otf}[Path=../Release/] \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 \varepsilon \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} } \NewDocumentCommand \CHESSSYMB { } { \fonttest_circled_aux:nn {"2654} {"265F} } \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. 2022-01-03} \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. Issues, bug reports, forks and other contributions are welcome. Please visit GitHub\footnote{https://github.com/YuanshengZhao/Garamond-Math/} for development details. A minimal example with \texttt{unicode-math} package is as following: \begin{verbatim} %Compile with `xelatex' command \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} The result should be \[x^3+y^3=z^3.\] \section{Alphabets \& StylisticSets} \subsubsection*{Latin and Greek (StylisticSet 4/5 give semi/extra bold for \texttt{\backslash symbf})} \[ \Latinalphabets\] \[ \latinalphabets \] \[ \symup{\Latinalphabets}\] \[ \symup{\latinalphabets} \] \[ \symbf{\Latinalphabets}\] \[ \symbf{\latinalphabets}\] \[ \symbfup{\Latinalphabets}\] \[ \symbfup{\latinalphabets} \] \[ \Greekalphabets \] \[\greekalphabets\] \[ \symup{\Greekalphabets} \] \[\symup{\greekalphabets} \] \[ \symbf{\Greekalphabets} \] \[\symbf{\greekalphabets} \] \[ \symbfup{\Greekalphabets}\] \[ \symbfup{\greekalphabets} \] \begingroup\mathversion{GaramondMathIV}\[\symbf{\Latinalphabets}\] \[\symbf{\latinalphabets}\]\endgroup \begingroup\mathversion{GaramondMathV}\[\symbf{\Latinalphabets}\] \[\symbf{\latinalphabets}\]\endgroup \subsubsection*{Sans and Typewriter: 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 $\rightarrow$ 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 $\rightarrow$ scaled CM; 8 $\rightarrow$ 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*{Fraktur: From Noto Sans Math\footnote{https://github.com/googlefonts/noto-fonts/}} \[ \symfrak{\Latinalphabets} \] \[\symfrak{\latinalphabets} \] \[ \symbffrak{\Latinalphabets} \] \[\symbffrak{\latinalphabets} \] \subsubsection*{Digits: Same width between weight and serif/sans} \[3.141592653589793238462643383279502884197169399375105820974944592307816406286\] \[\symsf{3.141592653589793238462643383279502884197169399375105820974944592307816406286}\] \[\symbf{3.141592653589793238462643383279502884197169399375105820974944592307816406286}\] \subsubsection*{\texttt{\backslash partial}: (StylisticSet 2 $\rightarrow$ 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 $\rightarrow$ horizontal bars)} \[\text{$\hbar$\qquad \begingroup\mathversion{GaramondMathVI} $\hbar$\endgroup}\] \subsubsection*{Italic $\symbf h$: (StylisticSet 10 $\rightarrow$ out-bending ones)} \[\text{$\displaystyle\hbar=\frac {\symbf{h}}{2\uppi} $\qquad \begingroup\mathversion{GaramondMathX} $\displaystyle\hbar=\frac {\symbf{h}}{2\uppi} $\endgroup}\] \subsubsection*{\texttt{\backslash tilde}: (StylisticSet 9 $\rightarrow$ ``normal'' ones)} \[\text{$\tilde F$\qquad \begingroup\mathversion{GaramondMathIX} $\tilde F$\endgroup}\] \subsubsection*{\texttt{\backslash int}: (StylisticSet 7 $\rightarrow$ 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 \subsubsection*{Binany Operators: (StylisticSet 11 $\rightarrow$ larger ones)} \[s=A+b\times 1\div x^3\] \begingroup\mathversion{GaramondMathXI}\[s=A+b\times 1\div x^3\]\endgroup \subsubsection*{Other Symbols} \begingroup \hspace{\parindent}\GaramondMath \CIRCLEDNUMA* \par \CIRCLEDNUMB* \par \CIRCLEDNUMC \par \CIRCLEDLETTERA \par \CIRCLEDLETTERB \par \CIRCLEDLETTERC \par \CHESSSYMB \endgroup \subsubsection*{Extensible Arrow Hack} The font contains the math table for constructing extensible arrow. However \texttt{unicode-math} does not provide an interface to that. In \LuaTeX ~one can use \texttt{\textbackslash Uhextensible}\footnote{https://tex.stackexchange.com/questions/423893/}. A more general solution is to add the following code in preamble. \begin{verbatim} \usepackage{extarrow} %or mathtools \makeatletter \renewcommand{\relbar}{\symbol{"E010}\mkern-.2mu\symbol{"E010}\mkern1.8mu} \renewcommand{\Relbar}{\symbol{"E011}\mkern-.2mu\symbol{"E011}\mkern1.8mu} \makeatother \end{verbatim} Then \texttt{\textbackslash xleftarrow} and other commands will work: \[\mathrm{CH}_3\mathrm{COO}\mathrm{H}+\mathrm{C}_2\mathrm{H}_5\mathrm{OH}\xrightarrow[{\triangle}]{\mathrm{H}_2\mathrm{SO}_4}\mathrm{CH}_3\mathrm{COOC}_2\mathrm{H}_5+\mathrm{H}_2\mathrm{O}.\] \section{Known Issue} \begin{itemize} \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} \[ 1 + 2 - 3 \times 4 \div 5 \pm 6 \mp 7 \dotplus 8 = -a \oplus b \otimes c -\{z\}\] \[\forall \epsilon, \exists \delta : x \in A \cup B \subset S \cap T \ntrianglerighteq U\] \[R_{\nu\kappa\lambda}^\mu=\partial_\kappa\Gamma_{\lambda\nu}^\mu-\partial_\lambda\Gamma_{\kappa\nu}^\mu+\Gamma_{\kappa\sigma}^\mu\Gamma_{\lambda\nu}^\sigma-\Gamma_{\lambda\sigma}^\mu\Gamma_{\kappa\nu}^\sigma\] \[T_{\alpha_1\cdots\alpha_k}'^{\beta_1\cdots\beta_l}=T_{i_1\cdots i_k}^{j_1\cdots j_l} \frac{\partial x^{i_1}}{\partial x'^{\alpha_1}}\cdots \frac{\partial x^{i_k}}{\partial x'^{\alpha_k}} \frac{\partial x'^{\beta_1}}{\partial x^{j_1}}\cdots \frac{\partial x'^{\beta_l}}{\partial x^{j_l}} \] \[\int_{\sqrt{\frac{1-m u+m\Delta/k^2}{2mu/k}}}^{X_p}\widehat{1+2+3+4}+\widetilde{5+6+7+8}\] \[ x \leftarrow y \leftrightarrow w \Rightarrow b \Leftrightarrow c \uparrow y \updownarrow w \Downarrow b \Updownarrow c \Searrow p \Swarrow p x \leftharpoonup x \upharpoonleft X \mapsfrom Y \mapsto Z \mapsup f \rightleftarrows f \updownarrows f h \rightthreearrows h \leftthreearrows p \] \[\int_0^1\frac{\ln (x+1)}{x}\dd{x}=\int_0^1\sum_{i=1}^{\infty}\frac{(-x)^{i-1}}{i}\dd{x}=\sum_{i=1}^{\infty}\int_0^1\frac{(-x)^{i-1}}{i}\dd{x}=\sum_{i=1}^{\infty}\frac{(-1)^{i+1}}{i^2}=\frac{\uppi^2}{12}\] \[ \int\limits_0^\infty \int_0^\infty \sum_{i=1}^\infty \prod_{j=i}^\infty \coprod_{k=i}^\infty \oiiint \varointclockwise \ointctrclockwise \awint \intclockwise \] \[ \Biggl( \biggl( \Bigl( \bigl( (x) \bigr) \Bigr) \biggr) \Biggr) \quad \Biggl[ \biggl[ \Bigl[ \bigl[ [x] \bigr] \Bigr] \biggr] \Biggr] \quad \Biggl\{ \biggl\{ \Bigl\{ \bigl\{ \{x\} \bigr\} \Bigr\} \biggr\} \Biggr\}\quad \Biggl\lvert \biggl\lvert \Bigl\lvert \bigl\lvert \lvert x\rvert \bigr\rvert \Bigr\rvert\biggr\rvert \Biggr\rvert\quad \Biggl\lVert \biggl\lVert \Bigl\lVert \bigl\lVert \lVert x\rVert \bigr\rVert \Bigr\rVert\biggr\rVert \Biggr\rVert\quad \Biggl\langle \biggl\langle \Bigl\langle \bigl\langle \langle x\rangle \bigr\rangle \Bigr\rangle\biggr\rangle \Biggr\rangle\quad \] \[ \Biggl\lgroup \biggl\lgroup \Bigl\lgroup \bigl\lgroup \lgroup x\rgroup \bigr\rgroup \Bigr\rgroup\biggr\rgroup \Biggr\rgroup\quad \Biggl\lfloor \biggl\lfloor \Bigl\lfloor \bigl\lfloor \lfloor x\rfloor \bigr\rfloor \Bigr\rfloor\biggr\rfloor \Biggr\rfloor\quad \Biggl\lceil \biggl\lceil \Bigl\lceil \bigl\lceil \lceil x\rceil \bigr\rceil \Bigr\rceil\biggr\rceil \Biggr\rceil\quad\] \[ \bra{x} + \ket{x} + \ip{\alpha}{\beta} + \op{\alpha}{\beta} + \bra{\frac{1}{2}} + \ket{\frac{1}{2}} + \ip{\frac{1}{2}}{\frac{1}{2}} + \op{\frac{1}{2}}{\frac{1}{2}} + \bra{\frac{a^2}{b^2}} + \Biggl\vert \frac{\ee^{x^2}}{\ee^{y^2}} \Biggr\rangle \] \[ \CIRCLEDNUMB + ABC^{\CIRCLEDNUMA} \] \[\left( \begin{matrix} {{u}_{0}} \\ {{u}_{1}} \\ \vdots \\ {{u}_{N-1}} \\ \end{matrix} \right)=\sum\limits_{k>0}{\left[ \left( \begin{matrix} 1 \\ \cos ka \\ \vdots \\ \cos k\left( N-1 \right)a \\ \end{matrix} \right)\underbrace{{{C}_{k+}}\cos ( {{\omega }_{k}}t+{{\varphi }_{k+}} )}_{\frac{2}{\sqrt{N}}{{q}_{k+}}}+\left( \begin{matrix} 0 \\ \sin ka \\ \vdots \\ \sin k\left( N-1 \right)a \\ \end{matrix} \right)\underbrace{{{C}_{k-}}\cos ( {{\omega }_{k}}t+{{\varphi }_{k-}} )}_{\frac{2}{\sqrt{N}}{{q}_{k-}}} \right]}\] \[ \begin{split} \mathcal{F}^{-1}(\kets{j}) &{}=\frac{1}{\sqrt{2^n}}\sum_{k=0}^{2^n-1}\exp\left(-2\uppi \ii \frac{jk}{2^n}\right)\kets{k}.\\ &{}=\frac{1}{\sqrt{2^n}}\sum_{k_{n-1}=0}^1\cdots\sum_{k_{0}=0}^1\exp\left(-2\uppi \ii j\sum_{l=0}^{n-1}\frac{2^l k_l}{2^n}\right)\kets{k_{n-1}\cdots k_0}\\ &{}=\frac{1}{\sqrt{2^n}}\sum_{k_{n-1}=0}^1\cdots\sum_{k_{0}=0}^1\bigotimes_{l=1}^n\left[\exp\left(-2\uppi \ii j\frac{k_{n-l}}{2^l}\right)\kets{k_{n-l}}\right]\\ &{}=\frac{1}{\sqrt{2^n}}\bigotimes_{l=1}^n\left[\sum_{k_{n-l}=0}^1\exp\left(-2\uppi \ii j\frac{k_{n-l}}{2^l}\right)\kets{k_{n-l}}\right]\\ &{}=\frac{1}{\sqrt{2^n}}\bigotimes_{l=1}^n\left[\kets{0}_{n-l}+\ee^{-2\uppi \ii j /2^l}\kets{1}_{n-l}\right]\\ &{}=\frac{1}{\sqrt{2^n}}\bigotimes_{l=1}^n\left[\kets{0}_{n-l}+\ee^{-2\uppi \ii (\overline{0.j_{l-1}\ldots j_0})}\kets{1}_{n-l}\right]. \end{split} \] \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}