Here is some LaTeX
Here is some ## \LaTeX ##.
$$ i\hbar\frac{\partial}{\partial t} \Psi(\mathbf{r},t) = \left [ \frac{-\hbar^2}{2\mu}\nabla^2 + V(\mathbf{r},t)\right ] \Psi(\mathbf{r},t) $$
The quadratic formula $$ x = {-b \pm \sqrt{b^2-4ac} \over 2a} $$
Cross product
$$
\mathbf{V}_1 \times \mathbf{V}_2 = \begin{pmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
\frac{\partial X}{\partial u} & \frac{\partial Y}{\partial u} & 0 \\
\frac{\partial X}{\partial v} & \frac{\partial Y}{\partial v} & 0
\end{pmatrix}
$$
Matrices (note verts and double verts don’t work and square brackets dont look right).
$$
p: \begin{pmatrix}1 & 0 \\ 0 & -1\end{pmatrix},
b: \begin{bmatrix}1 & 0 & 0 \\ 0 & -1 & 0 \\ & 0\end{bmatrix},
v: \begin{vmatrix}1 & 0 \\ 0 & -1\end{vmatrix}
$$
$$
B: \begin{Bmatrix}1 & 0 \\ 0 & -1\end{Bmatrix},
V: \begin{Vmatrix}1 & 0 \\ 0 & -1\end{Vmatrix}
$$
$$ 1 + \frac{q^2}{(1-q)}+\frac{q^6}{(1-q)(1-q^2)}+\cdots = \prod_{j=0}^{\infty}\frac{1}{(1-q^{5j+2})(1-q^{5j+3})}, \quad\quad \text{for $|q| < 1$}. $$