%%% UPDATED 3/3/2019

\usepackage{hyperref, amsmath, amsthm, latexsym, amsfonts, graphicx, enumerate, float, bm}

% quick set of natural numbers
\newcommand{\N}{\mathbb{N}}

% quick set integers
\newcommand{\Z}{\mathbb{Z}}

% quick set of real numbers
\newcommand{\R}{\mathbb{R}}

% quick set of rational numbers
\newcommand{\Q}{\mathbb{Q}}

% quick set of complex numbers
\newcommand{\C}{\mathbb{C}}

% partial derivative symbol
\newcommand{\dabba}{\partial}

% epsilon
\newcommand{\e}{\epsilon}

% blacksquare
\newcommand{\bs}{\blacksquare}

% Capital Psi
\newcommand{\IU}{\Psi}

% Lowercase psi
\newcommand{\U}{\psi}

% nth differentiation of one variable
\newcommand{\dv}[2][]{\frac{d^{#1}}{d{#2}^{#1}}}

% Variable of integration
\newcommand{\d}[2][]{\text{d}^{#1}#2}

% bold Nabla
\newcommand{\Na}{\bm{\nabla}}

% Nabla vector
\newcommand{\Nav}{\begin{bmatrix}\frac{\dabba}{\dabba x}\\ \frac{\dabba}{\dabba y}\\ \frac{\dabba}{\dabba z}\end{bmatrix}}

%sherical Nabla
\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}}


% Scalar-vector product
\newcommand{\scalVec}[4]{\begin{bmatrix}(#1)(#2)\\(#1)(#3)\\ (#1)(#4)\end{bmatrix}}

% gradient
\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}}

% Partial with given variable
\newcommand{\pt}[2][]{\frac{\dabba^{#1}}{\dabba #2^{#1}}}

% Divergence
\newcommand{\divergence}[3]{\pt{x}\left[#1\right]+\pt{y}\left[#2\right]+\pt{z}\left[#3\right]}

% Cross product 6 arguents
\newcommand{\cross}[6]{\begin{bmatrix}#2 #6-#3 #5\\ #3 #4-#1 #6\\ #1 #5-#2 #4\end{bmatrix}}

% Curl
\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}}

% infinite integral
\newcommand{\inint}{\int_{-\infty}^{\infty}}

% expectation Value
\newcommand{\xpctn}[1]{\left\langle#1\right\rangle}

% script L
\newcommand{\sL}{\mathcal{L}}

\newtheorem{theorem}{Theorem}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{remark}[theorem]{Remark}

\newtheorem*{theorem*}{Theorem}
\newtheorem*{lemma*}{Lemma}
\newtheorem*{definition*}{Definition}
\newtheorem*{corollary*}{Corollary}
\newtheorem*{remark*}{Remark}

\endinput