From 56ab99c6c9b2e537e73fc435df713c855143e3d5 Mon Sep 17 00:00:00 2001
From: Michael Wimmer <m.t.wimmer@tudelft.nl>
Date: Sun, 13 Sep 2020 21:43:53 +0200
Subject: [PATCH] fix some math
---
src/8_differential_equations_2.md | 6 +++---
1 file changed, 3 insertions(+), 3 deletions(-)
diff --git a/src/8_differential_equations_2.md b/src/8_differential_equations_2.md
index a94a60d..64830f3 100644
--- a/src/8_differential_equations_2.md
+++ b/src/8_differential_equations_2.md
@@ -198,7 +198,7 @@ $$f(x) = e^{\lambda_1 x}, \ x e^{\lambda_1 x} , \ \cdots, \ x^{m_{1}-1} e^{\lamb
since they are linear combinations of $f_1$ and $f_2$ which remain linearly
independent,
- $$\Tilde{f_1}(x)=cos(kx), \ \Tilde{f_2}(x)=sin{kx}.$$
+ $$\tilde{f_1}(x)=cos(kx), \tilde{f_2}(x)=sin{kx}.$$
**Case 2: $E<0$**
This time, define $E=-k^2$, for constant $k$. The characteristic polynomial
@@ -397,9 +397,9 @@ In the previous equation, the coefficient $A$ can be determined if the original
PDE was supplied with an initial condition.
Putting the solutions to the two ODEs together and redefining
-$\Tilde{A}=A \cdot c_1$, we arrive at the solutions for theb PDE,
+$\tilde{A}=A \cdot c_1$, we arrive at the solutions for theb PDE,
-$\psi_n(x,t) = \Tilde{A}_n e^{-i \frac{\lambda_n t}{\hbar}} sin(\frac{n \pi x}{L}).$
+$\psi_n(x,t) = \tilde{A}_n e^{-i \frac{\lambda_n t}{\hbar}} sin(\frac{n \pi x}{L}).$
Notice that there is one solution $\psi_{n}(x,t)$ for each natural number $n$.
These are still very special solutions. We will begin discussing next how to
--
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