diff options
author | Karl Berry <karl@freefriends.org> | 2023-01-16 21:11:39 +0000 |
---|---|---|
committer | Karl Berry <karl@freefriends.org> | 2023-01-16 21:11:39 +0000 |
commit | 7df0462240332030d967a22b5de31c5e666240d7 (patch) | |
tree | a6e2c3af563091c41eed8a589bc83b118004ec41 /Master | |
parent | 82cf5c68a439887b354b6410577f5a38fc93bc8b (diff) |
firamath-otf (16jan23)
git-svn-id: svn://tug.org/texlive/trunk@65561 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master')
-rw-r--r-- | Master/texmf-dist/doc/fonts/firamath-otf/Changes | 2 | ||||
-rw-r--r-- | Master/texmf-dist/doc/fonts/firamath-otf/README.md | 2 | ||||
-rw-r--r-- | Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.pdf | bin | 117979 -> 113783 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.tex | 168 | ||||
-rw-r--r-- | Master/texmf-dist/tex/latex/firamath-otf/firamath-otf.sty | 12 |
5 files changed, 30 insertions, 154 deletions
diff --git a/Master/texmf-dist/doc/fonts/firamath-otf/Changes b/Master/texmf-dist/doc/fonts/firamath-otf/Changes index 484c1119f31..a4f05106371 100644 --- a/Master/texmf-dist/doc/fonts/firamath-otf/Changes +++ b/Master/texmf-dist/doc/fonts/firamath-otf/Changes @@ -1,3 +1,5 @@ +0.03a 2023-01-16 - small changes to the doc +0.03 2023-01-11 - pass all unknown options to unicode-math 0.02a 2019-04-03 - fix for documentation 0.02 2019-03-21 - fix for missing weight default 0.01 2018-09-17 - first CTAN version diff --git a/Master/texmf-dist/doc/fonts/firamath-otf/README.md b/Master/texmf-dist/doc/fonts/firamath-otf/README.md index 68739ed80cf..b7c717a5e11 100644 --- a/Master/texmf-dist/doc/fonts/firamath-otf/README.md +++ b/Master/texmf-dist/doc/fonts/firamath-otf/README.md @@ -6,6 +6,6 @@ Package firamath-otf supports the free math font for Fira Sans % Either version 1.3 or, at your option, any later version. % % -% Copyright 2019- Herbert Voss hvoss@tug.org +% Copyright 2019-20... Herbert Voss hvoss@tug.org % diff --git a/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.pdf b/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.pdf Binary files differindex 5b2e7e1e2f1..6a322fb2357 100644 --- a/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.pdf +++ b/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.pdf diff --git a/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.tex b/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.tex index cc43c139b28..e671662497f 100644 --- a/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.tex +++ b/Master/texmf-dist/doc/fonts/firamath-otf/firamath-otf-doc.tex @@ -1,12 +1,13 @@ -%% $Id: firamath-otf-doc.tex 1022 2019-04-03 12:00:29Z herbert $ +%% $Id: firamath-otf-doc.tex 673 2023-01-16 19:44:41Z herbert $ \listfiles \documentclass[english,log-declarations=false]{article} -\usepackage{amsmath,esvect} +\usepackage{mathtools,esvect} \usepackage{FiraSans} \setmonofont{FiraMono}[ Numbers = {Monospaced}, Scale=MatchUppercase,FakeStretch=0.93] -\usepackage[fakebold]{firamath-otf} +\usepackage[fakebold,mathrm=sym]{firamath-otf} \usepackage{babel} +\everymath{}\everydisplay{}% FIX for current babel \usepackage{booktabs} \usepackage{xltabular} \usepackage{listings} @@ -16,7 +17,8 @@ \usepackage{xcolor,url} \usepackage{varioref,multido} \newcommand\Macro[1]{\texttt{\textbackslash#1}} -\usepackage{dtk-extern} +\usepackage{expl3} +\usepackage{hvextern} \newenvironment{demoquote} {\begingroup @@ -47,6 +49,7 @@ \def\PackageInfo#1#2{} \ExplSyntaxOn + \cs_new:Npn \__fonttest_close_msg:nn #1#2 { \msg_redirect_name:nnn {#1} {#2} { none } } \__fonttest_close_msg:nn { LaTeX / xparse } { not-single-char } @@ -240,14 +243,12 @@ \ExplSyntaxOff - +\def\Lcs#1{\texttt{\textbackslash #1}} \renewcommand\familydefault{\sfdefault} \DeclareMathOperator{\Div}{\symup{div}} \DeclareMathOperator{\Grad}{\symup{grad}} - - \title{OpenType math font Fira} \author{Herbert Voß} \usepackage{parskip} @@ -276,15 +277,18 @@ only the regular version has from todays update all symbols. Optional arguments are \begin{description} +%\item[\texttt{mathrm=sym}] Use characters from firamath for \Lcs{mathrm} \item[\texttt{fakebold}] Use faked bold symbols \item[\texttt{usefilenames}] Use filenames for the fonts instead of the symbolic font names \end{description} +All other unknown options, e.g. \verb|mathrm=sym| will be passed to the main package \texttt{unicode-math}. + The package itself loads by default \begin{verbatim} -\RequirePackage{ifxetex,ifluatex,xkeyval,textcomp} +\RequirePackage{iftex,xkeyval,textcomp} \RequirePackage{unicode-math} \end{verbatim} @@ -317,12 +321,12 @@ The package itself loads by default \end{align} \begin{align} - \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vec{v}\cdot\vec{v}\vec{n})\diff^2A &= 0\\ + \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vec{v}\cdot\vec{v}\vec{n}) \diff^2 A &= 0\\ \Q{}{t}\iiint\<\varrho\vec{v}\diff^3V+\oiint\varrho\vec{v}(\vec{v}\cdot\vec{n}\,)\diff^2A &= \iiint\<f_0\diff^3V+\oiint\vec{n}\cdot\TT\diff^2A \\ \Q{}{t}\iiint\<\left(\half v^2+e\right)\varrho\diff^3V+\oiint\left(\half v^2+e\right) \varrho\left(\vec{v}\cdot\vec{n}\,\right)\diff^2A & =\\ - \multispan2{\hfill${\displaystyle-\oiint\left(\vec{q}\cdot\vec{v}ec{n}\right)\diff^2A+ + \multispan2{\hfill${\displaystyle-\oiint\left(\vec{q}\cdot\vec{v}\vec{n}\right)\diff^2A+ \iiint\<\left(\vec{v}\cdot\vec{f}_0\right)\diff^3V+\oiint\left(\vec{v} \cdot\vec{n}~\TT\right)\diff^2A}$}.\nonumber \end{align} @@ -336,14 +340,13 @@ package \texttt{xfakebold} which writes some information into the created PDF to characters. For more informations see the documentation of \texttt{xfakebold}. \setBold -%\mathversion{bold} \begin{align} - \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vec{v}\cdot\vec{v}\vec{n})\diff^2A &= 0\\ + \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vec{v}\cdot\vec{v}ec{n})\diff^2A &= 0\\ \Q{}{t}\iiint\<\varrho\vec{v}\diff^3V+\oiint\varrho\vec{v}(\vec{v}\cdot\vec{n}\,)\diff^2A &= \iiint\<f_0\diff^3V+\oiint\vec{n}\cdot\symup{T}\diff^2A \\ \Q{}{t}\iiint\<\left(\half v^2+e\right)\varrho\diff^3V+\oiint\left(\half v^2+e\right) \varrho\left(\vec{v}\cdot\vec{n}\,\right)\diff^2A & =\\ - \multispan2{\hfill${\displaystyle-\oiint\left(\vec{q}\cdot\vec{v}\vec{n}\right)\diff^2A+ + \multispan2{\hfill${\displaystyle-\oiint\left(\vec{q}\cdot\vec{v}ec{n}\right)\diff^2A+ \iiint\<\left(\vec{v}\cdot\vec{f}_0\right)\diff^3V+\oiint\left(\vec{v} \cdot\vec{n}~\symup{T}\right)\diff^2A}$}.\nonumber \end{align} @@ -380,11 +383,11 @@ characters. For more informations see the documentation of \texttt{xfakebold}. \cdot\vec{n}~\TT\right)\diff^2A}$}.\nonumber \end{align} -\subsection{Version bold} - +\subsection{Version bold} \setBold + \begin{align} \Q{}{t}\iiint\<\varrho\diff^3V+\oiint\varrho(\vec{v}\cdot\vec{v}ec{n})\diff^2A &= 0\\ \Q{}{t}\iiint\<\varrho\vec{v}\diff^3V+\oiint\varrho\vec{v}(\vec{v}\cdot\vec{n}\,)\diff^2A &= @@ -395,6 +398,7 @@ characters. For more informations see the documentation of \texttt{xfakebold}. \iiint\<\left(\vec{v}\cdot\vec{f}_0\right)\diff^3V+\oiint\left(\vec{v} \cdot\vec{n}~\symup{T}\right)\diff^2A}$}.\nonumber \end{align} + \unsetBold @@ -807,138 +811,4 @@ characters. For more informations see the documentation of \texttt{xfakebold}. -\iffalse -\subsection{More Samples} - -\def\ee{\mathrm{e}} -\def\ii{\mathrm{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{\dd}{\,\mathrm{d}} -% \newcommand{\norm}[1]{\left\lVert{#1}\right\rVert} - -\[ g^{mn} g_{mn} T^{i}_{jk} \] - -\[ x \to \infty + \infty - \infty \] - -\begin{align*} - \int_{-\infty}^\infty \ee^{-x^2} \dd{x} - &= \qty[\int_{-\infty}^\infty \ee^{-x^2} \dd{x} \, \int_{-\infty}^\infty \ee^{-y^2} \dd{y}]^{1/2} \\ - &= \qty[\int_0^{2\pi} \int_0^\infty \ee^{-r^2} r \dd{r}\dd{\theta}]^{1/2} \\ - &= \qty[\pi \int_0^\infty \ee^{-u} \dd{u}]^{1/2} \\ - &= \sqrt{\pi} -\end{align*} - - -\begin{align*} -\int_{0}^aJ_0\left[\frac{x_n^{(0)}}{a}r\right]J_0\left[\frac{x_m^{(0)}}{a}r\right]r\dd{r}=\frac{a^2}{2}J_1^2[x_n^{(0)}]\delta_m^n.\\ -\int_{0}^{\infty}\frac{\cos x-\ee^{-x}}{x}\dd{x}=0\\ -\end{align*} -\[\oint_{\partial\Sigma}\vec E\cdot \dd{\vec{l}}=-\frac{1}{c}\frac{\dd}{\dd t}\iint_{\Sigma}\vec B \cdot \dd{\vec{S}};\] -\[\partial_{[a}F_{\beta\gamma]}=0;\quad \partial_\alpha F^{\alpha\beta}=\mu_0J^\beta\] -\[\left(\frac{-\hbar^2}{2m}\nabla^2+V\right)\Psi=i\hbar\dot{\Psi}\] -\[\begin{split} -\frac{1}{\mathcal{C}^2}&{}=\frac{\innerprod{g'}{g'}}{\mathcal{C}^2}=\sum_{\bm{k}}\sum_{\bm{k}'}\brakket{g}{c_{\bm{k}',\uparrow}^\dagger c_{\bm{k}',\downarrow} c_{\bm{k},\downarrow}^\dagger c_{\bm{k},\uparrow}}{g}=\sum_{\bm{k}}\brakket{g}{c_{\bm{k},\uparrow}^\dagger c_{\bm{k},\downarrow} c_{\bm{k},\downarrow}^\dagger c_{\bm{k},\uparrow}}{g}\\ -&{}=\sum_{\bm{k}}\brakket{g}{n_{\bm{k},\uparrow}\left(1-n_{\bm{k},\downarrow}\right)}{g}\\ -&{}=\sum_{\norm{\bm{k}}<k_F^\downarrow}\brakket{g}{0}{g}+\sum_{k_F^\downarrow<\norm{\bm{k}}<k_F^\uparrow}\brakket{g}{1}{g}+\sum_{\norm{\bm{k}}>k_F^\uparrow}\brakket{g}{0}{g}\\ -&{}=N_\uparrow-N_\downarrow -\end{split}\] -\[\left[ f,g \right]\equiv \sum_{\alpha =1}^{s}{\left( \frac{\partial f}{\partial {{q}_{\alpha }}}\frac{\partial g}{\partial {{p}_{\alpha }}}-\frac{\partial g}{\partial {{q}_{\alpha }}}\frac{\partial f}{\partial {{p}_{\alpha }}} \right)}=\sum\limits_{\alpha =1}^{s}{\begin{vmatrix} - \partial_{{q}_{\alpha }} f & \partial_{{p}_{\alpha }} f \\ - \partial_{{q}_{\alpha }} g & \partial_{{p}_{\alpha }} g \\ - \end{vmatrix} }=\sum\limits_{\alpha =1}^{s}{\frac{\partial \left( f,g \right)}{\partial \left( {{q}_{\alpha }},{{p}_{\alpha }} \right)}}\] -\[\begin{split} -& \frac{{{\text{d}}^{2}}f}{\text{d}{{t}^{2}}}=\frac{\text{d}}{\text{d}t}\left[ f,H \right]=\left[ \left[ f,H \right],H \right]=\hat{H}\hat{H}f={{{\hat{H}}}^{2}}f \\ -& \vdots \\ -& \frac{{{\text{d}}^{n}}f}{\text{d}{{t}^{n}}}=\underbrace{\left[ \left[ \left[ f,H \right],\cdots \right],H \right]}_{n}={{{\hat{H}}}^{n}}f \\ -\end{split}\] -\[\tilde{U}(r,z)=E_0\dfrac{\omega_0}{\omega(z)}\exp\left[-r^2\left(\dfrac{1}{\omega^2(z)}+\dfrac{\ii k}{2R(z)}\right)-\ii k z+\ii \zeta(z)\right]\] -\[\omega(z)=\omega_0\sqrt{1+\left(\dfrac{\lambda z}{\pi {\omega_0}^2}\right)^2};\quad R(z)=z\left[1+\left(\dfrac{\pi {\omega_0}^2}{\lambda z}\right)^2\right]\] -\[\left( \begin{matrix} -{mg}/{l}\;+k-m\omega _{1}^{2} & -k \\ --k & {mg}/{l}\;+k-m\omega _{1}^{2} \\ -\end{matrix} \right)\left( \begin{matrix} -{{a}_{11}} \\ -{{a}_{21}} \\ -\end{matrix} \right)=0\] -\[V=\underbrace{{{V}_{0}}}_{=0}+\underbrace{\sum\limits_{\alpha =1}^{s}{{{\left( \frac{\partial V}{\partial {{q}_{\alpha }}} \right)}_{0}}{{q}_{\alpha }}}}_{=0}+\underbrace{\frac{1}{2}\sum\limits_{\alpha ,\beta =1}^{s}{{{\left( \frac{{{\partial }^{2}}V}{\partial {{q}_{\alpha }}\partial {{q}_{\beta }}} \right)}_{0}}{{q}_{\alpha }}{{q}_{\beta }}}}_{>0}+\cdots \] -\[T=\frac{1}{2}\sum\limits_{i=1}^{n}{{{m}_{i}}{{{\dot{\bm r}}}_{i}}\cdot {{{\dot{\bm r}}}_{i}}}=\frac{1}{2}\sum\limits_{\alpha ,\beta =1}^{s}{\left[ \sum\limits_{i=1}^{n}{{{m}_{i}}{{\left( \frac{\partial {{\bm r}_{i}}}{\partial {{q}_{\alpha }}} \right)}_{0}}\cdot {{\left( \frac{\partial {{\bm r}_{i}}}{\partial {{q}_{\beta }}} \right)}_{0}}} \right]{{{\dot{q}}}_{\alpha }}{{{\dot{q}}}_{\beta }}}+\cdots \] -\[\left( \begin{matrix} -{{u}_{0}} \\ -{{u}_{1}} \\ -\vdots \\ -{{u}_{N-1}} \\ -\end{matrix} \right)=\sum\limits_{k>0}{\left[ \left( \begin{matrix} - 1 \\ - \cos ka \\ - \vdots \\ - \cos k\left( N-1 \right)a \\ - \end{matrix} \right)\underbrace{{{C}_{k+}}\cos \left( {{\omega }_{k}}t+{{\varphi }_{k+}} \right)}_{\frac{2}{\sqrt{N}}{{q}_{k+}}}+\left( \begin{matrix} - 0 \\ - \sin ka \\ - \vdots \\ - \sin k\left( N-1 \right)a \\ - \end{matrix} \right)\underbrace{{{C}_{k-}}\cos \left( {{\omega }_{k}}t+{{\varphi }_{k-}} \right)}_{\frac{2}{\sqrt{N}}{{q}_{k-}}} \right]}\] -\[G(\vec{r},{\vec{r}}',\tau )=\int _{-\infty }^{\infty }\tilde{G}(\vec{r},{\vec{r}}',\omega )e^{-i \tau \omega }d\omega=\int_{-\infty }^{\infty } \frac{e^{-i \tau \omega } e^{i k |\vec{r}-{\vec{r}}'| }}{(2 \pi ) |\vec{r}-{\vec{r}}'| } \, d\omega=\frac{\delta \left(\tau -\frac{R}{c}\right)}{|\vec{r}-{\vec{r}}'| }\] -\[ -\begin{split} -\mathcal{F}^{-1}(\ket{j}) -&{}=\frac{1}{\sqrt{2^n}}\sum_{k=0}^{2^n-1}\exp\left(-2\uppi \ii \frac{jk}{2^n}\right)\ket{k}.\\ -&{}=\frac{1}{\sqrt{2^n}}\sum_{k_{n-1}=0}^1\cdots\sum_{k_{0}=0}^1\exp\left(-2\uppi \ii j\sum_{l=0}^{n-1}\frac{2^l k_l}{2^n}\right)\ket{k_{n-1}\cdots k_0}\\ -&{}=\frac{1}{\sqrt{2^n}}\sum_{k_{n-1}=0}^1\cdots\sum_{k_{0}=0}^1\bigotimes_{l=1}^n\left[\exp\left(-2\uppi \ii j\frac{k_{n-l}}{2^l}\right)\ket{k_{n-l}}\right]\\ -&{}=\frac{1}{\sqrt{2^n}}\bigotimes_{l=1}^n\left[\sum_{k_{n-l}=0}^1\exp\left(-2\uppi \ii j\frac{k_{n-l}}{2^l}\right)\ket{k_{n-l}}\right]\\ -&{}=\frac{1}{\sqrt{2^n}}\bigotimes_{l=1}^n\left[\ket{0}_{n-l}+\ee^{-2\uppi \ii j /2^l}\ket{1}_{n-l}\right]\\ -&{}=\frac{1}{\sqrt{2^n}}\bigotimes_{l=1}^n\left[\ket{0}_{n-l}+\ee^{-2\uppi \ii ({0.j_{l-1}\ldots j_0})}\ket{1}_{n-l}\right]. -\end{split} -\] - -\newcommand{\lb}{\left(} -\newcommand{\rb}{\right)} -\newcommand{\ec}{\text{,}} -\newcommand{\ed}{\text{.}} -\newcommand{\bt}{\lb t\rb} -\newcommand{\deltaup}{\updelta} -\newcommand{\piup}{\uppi} -\newcommand{\ndd}{\,\mathrm{d}} -\subsubsection*{Problem 1} -For convenience, first we set $t_i=0$, and in the end, we replace $t_f$ by $t_f-t_i$ and right answer is obtained. -The classical path is \[x_c\lb t\rb=A \cos\omega t+B\sin \omega t\ec\]where $A$ and $B$ can be determined by plugging $\lb0,x_i\rb$ and $\lb t_f, x_f\rb$ into the equation. The result is -\[x_c\lb t\rb=x_i \cos\omega t+\frac{x_f-x_i\cos\omega t_f}{\sin\omega t_f}\sin \omega t\ed\] -We write $x\lb t\rb=x_c\lb t\rb+\deltaup x\bt$. Due to the fact that $\deltaup x$ should vanish at $t=0$ and $t=t_f$, $\deltaup x$ can be expanded as sine series: \[\deltaup x\bt=\sum_{n=1}^\infty a_n\sin\frac{n\piup t}{t_f}\ed\] -Also, the functional integral can be rewritten as \[\int\mathcal{D}\left[x\bt\right]=c\int\prod_{n=1}^\infty \dd a_n\ed\] -So, we have -\[L=\frac{m}{2}\lb\dot{x}_c+\deltaup\dot{x}\rb^2-\frac{m\omega^2}{2}\lb x_c+\deltaup x\rb^2\ec\] -\[\dot{x}\bt=-\omega x_i \sin\omega t +\omega \frac{x_f-x_i\cos\omega t_f}{\sin\omega t_f}\cos\omega t+\sum_{n=1}^\infty\frac{a_n n \piup}{t_f}\cos\frac{n \piup t}{t_f}\ec\] -\[S=\int_0^{t_f} L\ndd t\ed\] -Because $x_c$ is the classical path, $\deltaup S_\text{classical}=0$, so there can't be any the linear term in the expression of $S$, and we also have in mind that the sine and cosine series are orthogonal. So, we can write S as following: -\[\begin{split}S&{}=\frac{m}{2}\int_0^{t_f}\left[\lb-\omega x_i\sin\omega t+\omega \frac{x_f-x_i\cos\omega t_f}{\sin\omega t_f}\cos\omega t\rb^2+\sum_{n=1}^\infty\lb\frac{a_n n \piup}{t_f}\rb^2\cos^2\frac{n \piup t}{t_f}\right]\ndd t\\% -&\quad{}-\frac{m\omega^2}{2}\int_0^{t_f}\left[\lb x_i\cos\omega t+ \frac{x_f-x_i\cos\omega t_f}{\sin\omega t_f}\sin\omega t\rb^2+\sum_{n=1}^\infty {a_n}^2\sin^2\frac{n \piup t}{t_f}\right]\ndd t\\% -&{}=\sum_{n=1}^\infty\int_0^{t_f}\left[\frac{m}{2}\lb\frac{a_n n \piup}{t_f}\rb^2\cos^2\frac{n \piup t}{t_f}-\frac{m\omega^2}{2}{a_n}^2\sin^2\frac{n \piup t}{t_f}\right]\ndd t\\% -&\quad{}+\frac{m\omega^2}{2}\int_0^{t_f}\left[ {x_i}^2-\lb\frac{x_f-x_i\cos\omega t_f}{\sin\omega t_f}\rb^2\right]\lb\sin^2\omega t-\cos^2\omega t\rb\ndd t\\% -&\quad{}-\frac{m\omega^2}{2}\int_0^{t_f}4 {x_i}\lb\frac{x_f-x_i\cos\omega t_f}{\sin\omega t_f}\rb\lb\sin\omega t\cos\omega t\rb\ndd t\ed\end{split}\] -Using -\[\int_0^{t_f}\lb\sin^2\omega t-\cos^2\omega t\rb\ndd t=-\frac{\sin2\omega t_f}{2\omega}\ec\] -\[\int_0^{t_f}\sin\omega t\cdot\cos\omega t\ndd t=\frac{\sin^2\omega t_f}{2\omega}\ec\] -\[\int_0^{t_f}\sin^2\frac{n\piup t}{t_f} \ndd t=\int_0^{t_f}\cos^2\frac{n\piup t}{t_f} \ndd t=\frac{a_n n \piup}{t_f}\ec\] -we get -\[S=\sum_{n=1}^\infty\left[\frac{m}{2}\lb\frac{a_n n \piup}{t_f}\rb^2-\frac{m\omega^2}{2}{a_n}^2\right]\frac{t_f}{2}+\frac{m\omega}{2\sin\omega t_f}\left[\lb {x_i}^2+{x_f}^2\rb\cos\omega t_f-2 x_i x_f\right]\ed\] -\[\begin{split}U={}&\exp\left\{\frac{\ii}{\hbar}\frac{m\omega}{2\sin\omega t_f}\left[\lb {x_i}^2+{x_f}^2\rb\cos\omega t_f-2 x_i x_f\right]\right\}\\% -&{}\times c\prod_{n=1}^{\infty}\int_{-\infty}^\infty\exp{\frac{\ii}{\hbar}\left[\frac{m}{2}\lb\frac{n \piup}{t_f}\rb^2-\frac{m\omega^2}{2}\right]\frac{t_f {a_n}^2}{2}}\ndd a_n\ed\end{split}\] -Using the Fresnel integral formula: -\[\int_{-\infty}^\infty\exp\lb \ii t\rb\ndd t=\sqrt{\piup \ii}\ec\] -\[\int_{-\infty}^\infty\exp{\frac{\ii}{\hbar}\left[\frac{m}{2}\lb\frac{n \piup}{t_f}\rb^2-\frac{m\omega^2}{2}\right]\frac{t_f {a_n}^2}{2}}\ndd a_n\sim\frac{\sqrt{t_f}}{n}\ec\] -\[U\lb x_f,t_f;x_i,t_i\rb=c'\lb t_f-t_i\rb\exp\left\{\frac{\ii m\omega}{2\hbar\sin\left[\omega \lb t_f-t_i\rb\right]}\left[\lb {x_i}^2+{x_f}^2\rb\cos\left[\omega\lb t_f-t_i\rb\right]-2 x_i x_f\right]\right\}\ed\] -Because \[\int\dd x U\lb x_f,t_f;x,t\rb U\lb x,t;x_i,t_i\rb=U\lb x_f,t_f;x_i,t_i\rb\ec\] -By using the Fresnel integral again: -\[c'\lb t_f-t\rb c'\lb t-t_i\rb\sqrt{\frac{2 \piup \ii \hbar}{m \omega}\lb\frac{\cos\left[\omega\lb t_f-t\rb\right]}{\sin\left[\omega\lb t_f-t\rb\right]}+\frac{\cos\left[\omega\lb t-t_i\rb\right]}{\sin\left[\omega\lb t-t_i\rb\right]}\rb}=c'\lb t_f-t_i\rb\ec\] -\[c'\lb t_f-t_i\rb=\sqrt{\frac{m\omega}{2\piup \ii \hbar\sin\left[\omega\lb t_f-t_i\rb\right]}}\ed\] -Thus -\[\begin{split}U\lb x_f,t_f;x_i,t_i\rb=&\sqrt{\frac{m\omega}{2\piup \ii \hbar\sin\left[\omega\lb t_f-t_i\rb\right]}}\\&{}\times\exp\left\{\frac{\ii m\omega}{2\hbar\sin\left[\omega \lb t_f-t_i\rb\right]}\left[\lb {x_i}^2+{x_f}^2\rb\cos\left[\omega\lb t_f-t_i\rb\right]-2 x_i x_f\right]\right\}\ed\end{split}\] - - -\fi - - - \end{document} diff --git a/Master/texmf-dist/tex/latex/firamath-otf/firamath-otf.sty b/Master/texmf-dist/tex/latex/firamath-otf/firamath-otf.sty index ecc33046e86..41a56bd3fe7 100644 --- a/Master/texmf-dist/tex/latex/firamath-otf/firamath-otf.sty +++ b/Master/texmf-dist/tex/latex/firamath-otf/firamath-otf.sty @@ -1,4 +1,4 @@ -%% $Id: firamath-otf.sty 1022 2019-04-03 12:00:29Z herbert $ +%% $Id: firamath-otf.sty 673 2023-01-16 19:44:41Z herbert $ %% %% This file is distributed under the terms of the LaTeX Project Public %% License from CTAN archives in directory macros/latex/base/lppl.txt. @@ -8,10 +8,10 @@ % Copyright 2018 Herbert Voss hvoss@tug.org % \ProvidesPackage{firamath-otf}[% - 2019/04/03 v. 0.02a (Herbert Voss) Supports fira math fonts for all luatex/xetex .] + 2023/01/16 v. 0.03a (Herbert Voss) Supports fira math fonts for all luatex/xetex .] + +\RequirePackage{iftex,xkeyval,textcomp} -\RequirePackage{ifxetex,ifluatex,xkeyval,textcomp} -\RequirePackage{unicode-math} \newif\iffiramath@fakebold \firamath@fakeboldfalse \newif\iffiramath@lining \firamath@liningtrue @@ -42,8 +42,12 @@ \def\firamath@defaultfeatures{} \DeclareOptionX{defaultfeatures}{\def\firamath@defaultfeatures{#1}} +\DeclareOptionX*{\PassOptionsToPackage{\CurrentOption}{unicode-math}}% added 20230111 hv + \ProcessOptionsX\relax +\RequirePackage{unicode-math} + \iffiramath@fakebold\RequirePackage{xfakebold}\fi \iffiramath@lining \def\firamath@figurestyle{Lining} |