Homework for chapter 10 is done!
The follow equations were used, along with some for Dr. M. Smith, Professional Bad-Ass Calc professor.
Here is the rendering!
Here is the LaTeX.
\begin{enumerate}
\item $\psi (r,\theta, \phi) = \frac{1}{\sqrt{\pi}} \left ( {}\frac {1}{a_{0}} \right )^{3/2} e^{-r/a_{0}}$ \\
\item $\left | \psi (r) \right |^{2} 4\pi r^{2} dr$ \\
\item $P(r) = 4a_{0}^{-3}\int_{0}^{\infty} r^{2}e^{-2r/a_{0}}dr$ \\
\item $4 \pi r^{2}$ \\
\item $-\frac {\hbar ^{2}}{2m} \nabla^{2} \psi (\mathbf{r}) \hspace{6pt} + \hspace{6pt} U(\mathbf{r})\psi (\mathbf{r}) \hspace{pt6} = \hspace{6pt} E\psi(\mathbf{r})$ \\
\item $ -\frac {\hbar ^{2}}{2m} \nabla^{2} \psi (\mathbf{r}) \hspace{6pt} + \hspace{6pt} U(\mathbf{r})\psi (\mathbf{r}) \hspace{6pt} = \hspace{6pt} E\psi(\mathbf{r}) $ \\
\item $\nabla^{2} = \frac{\partial^2 }{\partial r^2} +\left ( \frac {2}{r} \right )\frac{\partial }{\partial r} +\frac{1}{r^{2}} \left [\frac{\partial^2 }{\partial \theta^2} +cot \theta \frac{\partial }{\partial
\theta}+ csc^{2}\theta \frac{\partial^2 }{\partial \phi^2} \right ] $ \\
\item $\nabla^{2} = \frac{\partial^2 }{\partial x^2} + \frac{\partial^2 }{\partial y^2} + \frac{\partial^2 }{\partial z^2} $ \\
\item $ \frac{\mathrm{d} }{\mathrm{d} v} n(v)dv = \frac{4\piN}{V}\left ( \frac{m}{2\pi K_{B}T} \right )^{\frac{3}{2}} \left \{ 2ve^ {\frac{-mv^{2}}{2K_{B}T}}+\frac{-2m}{2K_{B}T}v^{3}e^ {\frac{-mv^{2}}{2K_{B}T}}\right \}$ \\
\item $ $ \\
\item $ $ \\
\end{enumerate}
