LaTeXEx01


LaTeX Exercise 1

The images of the equations on this page were taken from the Wikipedia pages referenced for each equation.

Imports


In [16]:
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.

$f(x,\mu,\sigma)=\frac{1}{\sigma\sqrt{2\pi}}e^\frac{-(x-\mu)^2}{2\sigma^2}$ $\mu$ is the mean $\sigma$ is the 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 (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.

$\imath\hbar\frac{\partial}{\partial t}\Psi(r,t)=[\frac{-\hbar^2}{2\mu}\nabla^2+V(r,t)]\Psi(r,t)$ $\imath$ is the imaginary number $\Psi(r,t)$ is the wave function $\mu$ is the reduced mass of the particle $\nabla$ is the Laplacian operator $V(r,t)$ is the Potential Energy

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.

$\nabla f = \frac{1}{r^2}\frac{\partial}{\partial r}(r^2\frac{\partial f}{\partial r}) + \frac{1}{r^2\sin\theta} \frac{\partial}{\partial\theta}(\sin\theta\frac{\partial f}{\partial\theta})+\frac{1}{r^2\sin^2\theta} \frac{\partial^2 f}{\partial\psi^2}$

The variable r is the distannce from the origin and theta is the azimuth angle.