From 57e4d4889b4a10722afd1575e106e4b1348bfb82 Mon Sep 17 00:00:00 2001
From: Maciej Topyla <m.m.topyla@student.tudelft.nl>
Date: Sat, 3 Sep 2022 20:33:35 +0000
Subject: [PATCH] Wrapping a long equation in exercises
---
src/2_coordinates.md | 6 +++---
1 file changed, 3 insertions(+), 3 deletions(-)
diff --git a/src/2_coordinates.md b/src/2_coordinates.md
index e53b801..a9d5e8b 100644
--- a/src/2_coordinates.md
+++ b/src/2_coordinates.md
@@ -426,9 +426,9 @@ We have discussed four different coordinate systems:
In a similar fashion it can be shown that for spherical coordinates,
the Laplace operator acting on a function $\psi({\bf r})$ becomes:
- $$\nabla^2 \psi (r,\vartheta,\varphi) =
- \frac{1}{r^2} \frac{\partial}{\partial r^2} \left( r^2 \frac{\partial \psi(r,\vartheta,\varphi)}{\partial r} \right) + \frac{1}{r^2\sin^2\vartheta} \frac{\partial^2 \psi(r,\vartheta, \varphi)}{\partial \varphi^2} + \frac{1}{r^2\sin\vartheta}
- \frac{\partial}{\partial \vartheta}\left( \sin\vartheta \frac{\partial\psi(r,\vartheta, \varphi)}{\partial \vartheta}\right).$$
+ \begin{align} \nabla^2 \psi (r,\vartheta,\varphi) &=
+ \frac{1}{r^2} \frac{\partial}{\partial r^2} \left( r^2 \frac{\partial \psi(r,\vartheta,\varphi)}{\partial r} \right) \\ &+ \frac{1}{r^2\sin^2\vartheta} \frac{\partial^2 \psi(r,\vartheta, \varphi)}{\partial \varphi^2} \\ &+ \frac{1}{r^2\sin\vartheta}
+ \frac{\partial}{\partial \vartheta}\left( \sin\vartheta \frac{\partial\psi(r,\vartheta, \varphi)}{\partial \vartheta}\right).\end{align}
This is however even more tedious (you do not have to show this).
6. [:grinning:] *Integration and coordinates I*
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