From 5fcba1bfaf8821fbb01cc7e67e01c553ffebfa39 Mon Sep 17 00:00:00 2001
From: dependabot[bot] <49699333+dependabot[bot]@users.noreply.github.com>
Date: Fri, 19 Jul 2024 17:02:03 +0000
Subject: [PATCH] chore(deps): bump mdast-util-to-hast from 13.1.0 to 13.2.0 (#1279)

---
 docs/features/Latex.md |   11 +++++++++++
 1 files changed, 11 insertions(+), 0 deletions(-)

diff --git a/docs/features/Latex.md b/docs/features/Latex.md
index b2bdb2d..fdc9d27 100644
--- a/docs/features/Latex.md
+++ b/docs/features/Latex.md
@@ -39,6 +39,17 @@
 \end{bmatrix}
 $$
 
+$$
+\begin{array}{rll}
+E \psi &= H\psi & \text{Expanding the Hamiltonian Operator} \\
+&= -\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2} \psi + \frac{1}{2}m\omega x^2 \psi & \text{Using the ansatz $\psi(x) = e^{-kx^2}f(x)$, hoping to cancel the $x^2$ term} \\
+&= -\frac{\hbar^2}{2m} [4k^2x^2f(x)+2(-2kx)f'(x) + f''(x)]e^{-kx^2} + \frac{1}{2}m\omega x^2 f(x)e^{-kx^2} &\text{Removing the $e^{-kx^2}$ term from both sides} \\
+& \Downarrow \\
+Ef(x) &= -\frac{\hbar^2}{2m} [4k^2x^2f(x)-4kxf'(x) + f''(x)] + \frac{1}{2}m\omega x^2 f(x) & \text{Choosing $k=\frac{im}{2}\sqrt{\frac{\omega}{\hbar}}$ to cancel the $x^2$ term, via $-\frac{\hbar^2}{2m}4k^2=\frac{1}{2}m \omega$} \\
+&= -\frac{\hbar^2}{2m} [-4kxf'(x) + f''(x)] \\
+\end{array}
+$$
+
 > [!warn]
 > Due to limitations in the [underlying parsing library](https://github.com/remarkjs/remark-math), block math in Quartz requires the `$$` delimiters to be on newlines like above.
 

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