\documentclass[12pt]{article}
\newcommand{\vs}{\vspace{.1in}}
\newcommand{\ds}{\displaystyle}
\newcommand{\p}{\partial}
\newcommand{\Tr}{\rm Tr}
\usepackage[T1]{fontenc}
\usepackage{yfonts}
\usepackage{graphicx}
\usepackage{latexsym}
\usepackage{amsmath}
\usepackage{amssymb}
\def\Dirac{\not\hspace{-1.50mm}\partial}
\def\DDirac{\not\hspace{-1.50mm}D}

\usepackage{amsfonts}
\usepackage{rawfonts}
\usepackage{amsxtra}
\usepackage{amscd}
\usepackage{amsthm}
\usepackage{eucal}

%\usepackage{tikz}
%\usetikzlibrary{arrows,decorations.pathmorphing,decorations.markings,trees,backgrounds,fit,calc,through}
\usepackage{slashed}
\input{prepictex}
\input{pictex}
\input{postpictex}
\begin{document}

\noindent{L \it Schr\"{o}dinger's Equation:}
$$ i\hbar \frac{\ds \partial\psi}{\ds \partial t} = 
-\frac{\ds \hbar^2}{\ds 2m} \nabla^2\psi + V\psi$$

\vs

\noindent{M. \it Dirac Equation:}


$$
\left(i\DDirac - m\right)  \psi=0
$$
\vs

\noindent{N. \it Atiyah-Singer Theorem for Twisted Dirac Operator:} 


$$\dim \ker \slash \! \! \! \! {D}_E - \dim \mbox{coker}~  
\slash \! \! \! \! {D}_E = \int_M \hat{A}(M) \cdot ch (E)$$
\vs



\end{document}