From 4081931a8c0437ab5a2104f9b83caf2f8098de65 Mon Sep 17 00:00:00 2001
From: Michael Wimmer <m.t.wimmer@tudelft.nl>
Date: Tue, 15 Sep 2020 22:18:39 +0200
Subject: [PATCH] fix more 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 22f6d3c..05dcf0b 100644
--- a/src/8_differential_equations_2.md
+++ b/src/8_differential_equations_2.md
@@ -489,12 +489,12 @@ the eigenfunctions of $L$.
Recall that q quantum state $|\phi\rangle$ can be written in an orthonormal
basis $\{ |u_n\rangle \}$ as
- $$\|\phi\rangle = \underset{n}{\Sigma} \langle u_n | \phi \rangle\, |u_n\rangle.$$
+ $$|\phi\rangle = \underset{n}{\Sigma} \langle u_n | \phi \rangle\, |u_n\rangle.$$
In terms of hermitian operators and their eigenfunctions, the eigenfunctions
play the role of the orthonormal basis. In reference to our running example,
the 1D Schrödinger equation of a free particle, the eigenfunctions
- $\sin(\frac{n \pi x}{L})$ play the role of the basis functions $\ket{u_n}$.
+ $\sin(\frac{n \pi x}{L})$ play the role of the basis functions $|u_n\rangle$.
To close our running example, consider the initial condition
$\psi(x,o) = \psi_{0}(x)$. Since the eigenfunctions $\sin(\frac{n \pi x}{L})$
@@ -583,7 +583,7 @@ necessary to work with numerical methods of solution.
6. [:sweat:] We consider the Hilbert space of functions $f(x)$ defined
for $x \ \epsilon \ [0,L]$ with $f(0)=f(L)=0$.
- Which of the following operators on this space is hermitian?
+ Which of the following operators on this space is Hermitian?
(a) $L = A(x) \frac{d^2 f}{dx^2}$
--
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