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'

---
 .../know/concept/fermi-dirac-distribution/index.md | 32 +++++++++++-----------
 1 file changed, 16 insertions(+), 16 deletions(-)

(limited to 'source/know/concept/fermi-dirac-distribution')

diff --git a/source/know/concept/fermi-dirac-distribution/index.md b/source/know/concept/fermi-dirac-distribution/index.md
index ea1f8b8..09a3e76 100644
--- a/source/know/concept/fermi-dirac-distribution/index.md
+++ b/source/know/concept/fermi-dirac-distribution/index.md
@@ -13,12 +13,12 @@ layout: "concept"
 which obey the [Pauli exclusion principle](/know/concept/pauli-exclusion-principle/),
 will distribute themselves across the available states in a system at equilibrium.
 
-Consider one single-particle state $s$,
-which can contain $0$ or $1$ fermions.
-Because the occupation number $N$ is variable,
+Consider one single-particle state $$s$$,
+which can contain $$0$$ or $$1$$ fermions.
+Because the occupation number $$N$$ is variable,
 we turn to the [grand canonical ensemble](/know/concept/grand-canonical-ensemble/),
-whose grand partition function $\mathcal{Z}$ is as follows,
-where we sum over all microstates of $s$:
+whose grand partition function $$\mathcal{Z}$$ is as follows,
+where we sum over all microstates of $$s$$:
 
 $$\begin{aligned}
     \mathcal{Z}
@@ -26,12 +26,12 @@ $$\begin{aligned}
     = 1 + \exp(- \beta (\varepsilon - \mu))
 \end{aligned}$$
 
-Where $\mu$ is the chemical potential,
-and $\varepsilon$ is the energy contribution per particle in $s$,
-i.e. the total energy of all particles $E = \varepsilon N$.
+Where $$\mu$$ is the chemical potential,
+and $$\varepsilon$$ is the energy contribution per particle in $$s$$,
+i.e. the total energy of all particles $$E = \varepsilon N$$.
 
 The corresponding [thermodynamic potential](/know/concept/thermodynamic-potential/)
-is the Landau potential $\Omega$, given by:
+is the Landau potential $$\Omega$$, given by:
 
 $$\begin{aligned}
     \Omega
@@ -39,8 +39,8 @@ $$\begin{aligned}
     = - k T \ln\!\Big( 1 + \exp(- \beta (\varepsilon - \mu)) \Big)
 \end{aligned}$$
 
-The average number of particles $\Expval{N}$
-in state $s$ is then found to be as follows:
+The average number of particles $$\Expval{N}$$
+in state $$s$$ is then found to be as follows:
 
 $$\begin{aligned}
     \Expval{N}
@@ -49,9 +49,9 @@ $$\begin{aligned}
     = \frac{\exp(- \beta (\varepsilon - \mu))}{1 + \exp(- \beta (\varepsilon - \mu))}
 \end{aligned}$$
 
-By multiplying both the numerator and the denominator by $\exp(\beta (\varepsilon \!-\! \mu))$,
+By multiplying both the numerator and the denominator by $$\exp(\beta (\varepsilon \!-\! \mu))$$,
 we arrive at the standard form of
-the **Fermi-Dirac distribution** or **Fermi function** $f_F$:
+the **Fermi-Dirac distribution** or **Fermi function** $$f_F$$:
 
 $$\begin{aligned}
     \boxed{
@@ -61,9 +61,9 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-This tells the expected occupation number $\Expval{N}$ of state $s$,
-given a temperature $T$ and chemical potential $\mu$.
-The corresponding variance $\sigma^2$ of $N$ is found to be:
+This tells the expected occupation number $$\Expval{N}$$ of state $$s$$,
+given a temperature $$T$$ and chemical potential $$\mu$$.
+The corresponding variance $$\sigma^2$$ of $$N$$ is found to be:
 
 $$\begin{aligned}
     \boxed{
-- 
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