Macros

$\newcommand{\DD}[2][]{\frac{d^2 #1}{d#2^2}}\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}\newcommand{\dd}[2][]{\frac{d#1}{d#2}}\newcommand{\pp}[2][]{\frac{\partial#1}{\partial #2}}\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$