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%%% UPDATED 3/3/201912\usepackage{hyperref, amsmath, amsthm, latexsym, amsfonts, graphicx, enumerate, float, bm}34% quick set of natural numbers5\newcommand{\N}{\mathbb{N}}67% quick set integers8\newcommand{\Z}{\mathbb{Z}}910% quick set of real numbers11\newcommand{\R}{\mathbb{R}}1213% quick set of rational numbers14\newcommand{\Q}{\mathbb{Q}}1516% quick set of complex numbers17\newcommand{\C}{\mathbb{C}}1819% partial derivative symbol20\newcommand{\dabba}{\partial}2122% epsilon23\newcommand{\e}{\epsilon}2425% blacksquare26\newcommand{\bs}{\blacksquare}2728% Capital Psi29\newcommand{\IU}{\Psi}3031% Lowercase psi32\newcommand{\U}{\psi}3334% nth differentiation of one variable35\newcommand{\dv}[2][]{\frac{d^{#1}}{d{#2}^{#1}}}3637% Variable of integration38\newcommand{\d}[2][]{\text{d}^{#1}#2}3940% bold Nabla41\newcommand{\Na}{\bm{\nabla}}4243% Nabla vector44\newcommand{\Nav}{\begin{bmatrix}\frac{\dabba}{\dabba x}\\ \frac{\dabba}{\dabba y}\\ \frac{\dabba}{\dabba z}\end{bmatrix}}4546%sherical Nabla47\newcommand{\NaSph}{\hat{e}_r\pt{r}+\hat{e}_\theta\frac{1}{r}\pt{\theta}+\hat{e}_\phi\frac{1}{r\sin(\theta)}\pt{\phi}}484950% Scalar-vector product51\newcommand{\scalVec}[4]{\begin{bmatrix}(#1)(#2)\\(#1)(#3)\\ (#1)(#4)\end{bmatrix}}5253% gradient54\newcommand{\gradient}[1]{\begin{bmatrix}\frac{\dabba}{\dabba x}\left[#1\right]\\ \frac{\dabba}{\dabba y}\left[#1\right]\\ \frac{\dabba}{\dabba z}\left[#1\right]\end{bmatrix}}5556% Partial with given variable57\newcommand{\pt}[2][]{\frac{\dabba^{#1}}{\dabba #2^{#1}}}5859% Divergence60\newcommand{\divergence}[3]{\pt{x}\left[#1\right]+\pt{y}\left[#2\right]+\pt{z}\left[#3\right]}6162% Cross product 6 arguents63\newcommand{\cross}[6]{\begin{bmatrix}#2 #6-#3 #5\\ #3 #4-#1 #6\\ #1 #5-#2 #4\end{bmatrix}}6465% Curl66\newcommand{\curl}[3]{\begin{bmatrix}\pt{y}\left[#3\right]-\pt{z}\left[#2\right]\\ \pt{z}\left[#1\right]-\pt{x}\left[#3\right]\\ \pt{x}\left[#2\right]-\pt{y}\left[#1\right]\end{bmatrix}}6768% infinite integral69\newcommand{\inint}{\int_{-\infty}^{\infty}}7071% expectation Value72\newcommand{\xpctn}[1]{\left\langle#1\right\rangle}7374% script L75\newcommand{\sL}{\mathcal{L}}7677\newtheorem{theorem}{Theorem}78\newtheorem{lemma}[theorem]{Lemma}79\newtheorem{definition}[theorem]{Definition}80\newtheorem{corollary}[theorem]{Corollary}81\newtheorem{remark}[theorem]{Remark}8283\newtheorem*{theorem*}{Theorem}84\newtheorem*{lemma*}{Lemma}85\newtheorem*{definition*}{Definition}86\newtheorem*{corollary*}{Corollary}87\newtheorem*{remark*}{Remark}8889\endinput9091