Including beautifully rendered equations is easy in Org Mode.

It was as simple as surrounding the question by dollar signs: $\psi (t)$ which appears on my screen as \(\psi(t)\).

You can wrap them with \begin{equation} ... \end{equation} like

\begin{equation}
  i \hbar \frac{\partial}{\partial t}\left|\psi (t)\right\rangle = \hat{H} \left|\psi (t)\right\rangle
\end{equation}

will produce

\begin{equation} i \hbar \frac{\partial}{\partial t}\left|\psi (t)\right\rangle = \hat{H} \left|\psi (t)\right\rangle \end{equation}

Previewing as you write

RTFM to understand what is going on, but

C-c C-x C-l (org-latex-preview)
Produce a preview image of the LaTeX fragment at point and overlay it over the source code. If there is no fragment at point, process all fragments in the current entry—between two headlines.

When called with a single prefix argument, clear all images in the current entry. Two prefix arguments produce a preview image for all fragments in the buffer, while three of them clear all the images in that buffer.

Automatically displaying equations

For standard Org documents (for example Org Roam notes) you should add #+startup: latexpreview at the start of the file.

For example, the following note for the Schrödinger equation has the command at line 5:

1
2
3
4
5
6
7
8
9

:PROPERTIES:
:ID:       1238BA43-EBAA-4D44-F54D-BEEF9E636548
:END:
#+title: Schrödinger equation
#+startup: latexpreview

\begin{equation}
  i \hbar \frac{\partial}{\partial t}\left|\psi (t)\right\rangle = \hat{H} \left|\psi (t)\right\rangle
\end{equation}

For Hugo posts

My Hugo posts are created converting org \(\to\) markdown \(\to\) HTML. However, all that is needed is adding line 4 to the properties drawer, as shown below:

1
2
3
4
5

:PROPERTIES:
:EXPORT_FILE_NAME: price-forecasts-comparison
:EXPORT_DATE: 2019-01-27T20:43:00+10:00
:export_hugo_custom_front_matter: :math true
:END:

However, for Hugo we should be wrapping the equations in \( ... \).