<jupyter_start><jupyter_text>LaTeX Exercise 1 The images of the equations on this page were taken from the Wikipedia pages referenced for each equation.  Imports<jupyter_code>from IPython.display import Image<jupyter_output><empty_output><jupyter_text>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](http://en.wikipedia.org/wiki/Normal_distribution). Following the main equation, write a sentence that defines all of the variable in the equation.<jupyter_code>Image(filename='normaldist.png')<jupyter_output><empty_output><jupyter_text>YOUR ANSWER HERE: \begin{equation*}\Large{f(x, \mu, \sigma) = \frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}}\end{equation*};     $\mu$ = the mean or expectaion of distribution.;     x = position;     $\sigma$ = standard deviation. In the following cell, use Markdown and LaTeX to typeset the equation for the time-dependent Schrodinger equation for non-relativistic particles shown [here](http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equationTime-dependent_equation) (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.<jupyter_code>Image(filename='tdseqn.png')<jupyter_output><empty_output><jupyter_text>YOUR ANSWER HERE:$\large{i\hbar \frac{\partial}{\partial t}\Psi(r,t) = \left[\frac{-\hbar^2}{2\mu}\nabla^2 + V(r,t) \right]\Psi(r,t)}$;     $\mu$ = particles reduced mass;    $V$ = potential energy;     $\nabla^2$ = laplacian;     $\Psi$ = position-space wave function. 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](http://en.wikipedia.org/wiki/Laplace_operatorTwo_dimensions). Following the main equation, write a sentence that defines all of the variable in the equation.<jupyter_code>Image(filename='delsquared.png')<jupyter_output><empty_output><jupyter_text>YOUR ANSWER HERE:$\large{\Delta f = \frac{1}{r^2}\frac{\partial}{\partial r} \left(r^2 \frac{\partial f}{\partial r} \right) + \frac{1}{r^2 \text{sin} \theta}\frac{\partial}{\partial \theta} \left(\text{sin} \theta \frac{\partial f}{\partial \theta} \right) + \frac{1}{r^2 \text{sin}^2 \theta}\frac{\partial ^2 f}{\partial \psi ^2}}$;    $r$ = distance from origin;      $\theta$ = zenith angle (angle from z-axis);     $\psi$ = should be $\phi$, azimuthal angle (angle around xy-plane).<jupyter_code>I changed the font size to make it easier to read.<jupyter_output><empty_output>
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