From 16555851b6514a736c5c9d8e73de7da7fc9b6288 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Thu, 20 Oct 2022 18:25:31 +0200
Subject: Migrate from 'jekyll-katex' to 'kramdown-math-sskatex'

---
 source/know/concept/dirac-notation/index.md | 22 +++++++++++-----------
 1 file changed, 11 insertions(+), 11 deletions(-)

(limited to 'source/know/concept/dirac-notation')

diff --git a/source/know/concept/dirac-notation/index.md b/source/know/concept/dirac-notation/index.md
index 8861505..46cc325 100644
--- a/source/know/concept/dirac-notation/index.md
+++ b/source/know/concept/dirac-notation/index.md
@@ -12,16 +12,16 @@ layout: "concept"
 without needing to worry about the space's representation. It is
 basically the *lingua franca* of quantum mechanics.
 
-In Dirac notation there are **kets** $\Ket{V}$ from the Hilbert space
-$\mathbb{H}$ and **bras** $\Bra{V}$ from a dual $\mathbb{H}'$ of the
+In Dirac notation there are **kets** $$\Ket{V}$$ from the Hilbert space
+$$\mathbb{H}$$ and **bras** $$\Bra{V}$$ from a dual $$\mathbb{H}'$$ of the
 former. Crucially, the bras and kets are from different Hilbert spaces
 and therefore cannot be added, but every bra has a corresponding ket and
 vice versa.
 
 Bras and kets can be combined in two ways: the **inner product**
-$\Inprod{V}{W}$, which returns a scalar, and the **outer product**
-$\Ket{V} \Bra{W}$, which returns a mapping $\hat{L}$ from kets $\Ket{V}$
-to other kets $\Ket{V'}$, i.e. a linear operator. Recall that the
+$$\Inprod{V}{W}$$, which returns a scalar, and the **outer product**
+$$\Ket{V} \Bra{W}$$, which returns a mapping $$\hat{L}$$ from kets $$\Ket{V}$$
+to other kets $$\Ket{V'}$$, i.e. a linear operator. Recall that the
 Hilbert inner product must satisfy:
 
 $$\begin{aligned}
@@ -29,7 +29,7 @@ $$\begin{aligned}
 \end{aligned}$$
 
 So far, nothing has been said about the actual representation of bras or
-kets. If we represent kets as $N$-dimensional columns vectors, the
+kets. If we represent kets as $$N$$-dimensional columns vectors, the
 corresponding bras are given by the kets' adjoints, i.e. their transpose
 conjugates:
 
@@ -45,7 +45,7 @@ $$\begin{aligned}
     \end{bmatrix}
 \end{aligned}$$
 
-The inner product $\Inprod{V}{W}$ is then just the familiar dot product $V \cdot W$:
+The inner product $$\Inprod{V}{W}$$ is then just the familiar dot product $$V \cdot W$$:
 
 $$\begin{gathered}
     \Inprod{V}{W}
@@ -60,7 +60,7 @@ $$\begin{gathered}
     = v_1^* w_1 + ... + v_N^* w_N
 \end{gathered}$$
 
-Meanwhile, the outer product $\Ket{V} \Bra{W}$ creates an $N \cross N$ matrix:
+Meanwhile, the outer product $$\Ket{V} \Bra{W}$$ creates an $$N \cross N$$ matrix:
 
 $$\begin{gathered}
     \Ket{V} \Bra{W}
@@ -80,9 +80,9 @@ $$\begin{gathered}
     \end{bmatrix}
 \end{gathered}$$
 
-If the kets are instead represented by functions $f(x)$ of
-$x \in [a, b]$, then the bras represent *functionals* $F[u(x)]$ which
-take an unknown function $u(x)$ as an argument and turn it into a scalar
+If the kets are instead represented by functions $$f(x)$$ of
+$$x \in [a, b]$$, then the bras represent *functionals* $$F[u(x)]$$ which
+take an unknown function $$u(x)$$ as an argument and turn it into a scalar
 using integration:
 
 $$\begin{aligned}
-- 
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