%
%     Macro Definitions for LaTeX Math Functions
%


\newcommand\delx [2] {{ \frac {\partial {#1}} {\partial {#2}} }}


\newcommand\delxn [3] {
     { \frac {{\partial}^{#1}{#2}} {{\partial{#3}^{#1}}}}
                    }




\newcommand\inv [1] { { \frac {1} {{#1}}}}

\newcommand\bra [1] {\left\langle {#1} \right\mid }

\newcommand\ket [1] {\left\mid {#1} \right\rangle }

\newcommand\braket [2] {\left\langle {#1} \mid {#2} \right\rangle}

\newcommand\mtrxel [3] {\left\langle {#1} \mid {#2} \mid {#3} \right\rangle}


\newcommand\first { 1$^{st}$ }

\newcommand\second { 2$^{nd}$ }

\newcommand\fourth { 4$^{th}$ }

\newcommand\third { 3$^{rd}$ }


\newcommand\boxit [1] {\vbox
                   {\hrule \hbox
                     {\vrule \hskip 1pt \kern3pt 
                        \vbox{\vskip 1pt \kern3pt #1 \kern3pt \vskip 2pt}
                       \kern1pt\vrule}
                    \hrule}
                  }