```
In [1]:
```from IPython.display import Image

```
In [2]:
```Image(filename='normaldist.png')

```
Out[2]:
```

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

The above equation is the probability density for x, where $\mu$ represents the mean of the distribution, and $\sigma$ is the standard deviation with $\sigma^{2}$ being the variance.

```
In [3]:
```Image(filename='tdseqn.png')

```
Out[3]:
```

\begin{equation*}
i\bar{h}\frac{\partial}{\partial t} \Psi (\mathbf{r},t) = \left[\frac{-h^{2}}{2\mu}\Delta^{2} + V(\mathbf{r},t)\right]\Psi(\mathbf{r},t)
\end{equation*}

In the above equation i is an imaginary unit, $\bar{h}$ is placks constant divided by 2$\pi$, $\Psi$ is the quantum wave function of the system, $\mu$ is the reduced mass, $\Delta^{2}$ is the Laplace operator, and V is the potential energy.

```
In [4]:
```Image(filename='delsquared.png')

```
Out[4]:
```

\begin{equation*}
\Delta f =\frac{1}{r^{2}}\frac{\partial}{\partial r} \left(r^{2} \frac{\partial}{\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\varphi^{2}}
\end{equation*}

In the above equation $\theta$ represents is the zenith angle and $\varphi$ is the azimuthal angle

```
In [ ]:
```