# LaTeX Exercise 1

## Imports



In :

from IPython.display import Image



## Typesetting equations

In the following cell, use Markdown and LaTeX to typeset the equation for the probability density of the normal distribution $f(x, \mu, \sigma)$, which can be found here. Following the main equation, write a sentence that defines all of the variable in the equation.



In :

Image(filename='normaldist.png')




Out:


\begin{equation*} f(x,\mu,\sigma) = \frac{1} {\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}} \end{equation*}

In the following cell, use Markdown and LaTeX to typeset the equation for the time-dependent Schrodinger equation for non-relativistic particles shown here (use the version that includes the Laplacian and potential energy). Following the main equation, write a sentence that defines all of the variable in the equation.



In :

Image(filename='tdseqn.png')




Out:


\begin{equation*} 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) \end{equation*}

In the following cell, use Markdown and LaTeX to typeset the equation for the Laplacian squared ($\Delta=\nabla^2$) acting on a scalar field $f(r,\theta,\phi)$ in spherical polar coordinates found here. Following the main equation, write a sentence that defines all of the variable in the equation.



In :

Image(filename='delsquared.png')




Out:


\begin{equation*} \triangle f = \frac{1}{r^2} \frac{\partial}{\partial{r}} \left( r^2\frac{\partial{f}}{\partial{r}} \right) + \frac{1}{r^2 \sin{\theta}} \frac{\partial}{\partial{\theta}} \left( \sin{\theta} \frac{\partial{f}}{\partial{\theta}} \right) + \frac {1}{r^2 \sin^2 \theta} \frac{\partial^2{f}}{\partial^2 \varphi^2} \end{equation*}


In [ ]: