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diff --git a/source/know/concept/maxwell-bloch-equations/index.md b/source/know/concept/maxwell-bloch-equations/index.md
index 8ba9a5b..b306c7d 100644
--- a/source/know/concept/maxwell-bloch-equations/index.md
+++ b/source/know/concept/maxwell-bloch-equations/index.md
@@ -12,7 +12,7 @@ layout: "concept"
 ---
 
 For an electron in a two-level system with time-independent states
-$\Ket{g}$ (ground) and $\Ket{e}$ (excited),
+$$\Ket{g}$$ (ground) and $$\Ket{e}$$ (excited),
 consider the following general solution
 to the full Schrödinger equation:
 
@@ -23,9 +23,9 @@ $$\begin{aligned}
 
 Perturbing this system with
 an [electromagnetic wave](/know/concept/electromagnetic-wave-equation/)
-introduces a time-dependent sinusoidal term $\hat{H}_1$ to the Hamiltonian.
+introduces a time-dependent sinusoidal term $$\hat{H}_1$$ to the Hamiltonian.
 In the [electric dipole approximation](/know/concept/electric-dipole-approximation/),
-$\hat{H}_1$ is given by:
+$$\hat{H}_1$$ is given by:
 
 $$\begin{aligned}
     \hat{H}_1(t)
@@ -38,10 +38,10 @@ $$\begin{aligned}
     = \vb{E}_0 \cos(\omega t)
 \end{aligned}$$
 
-Where $\vb{E}$ is an [electric field](/know/concept/electric-field/),
-and $\hat{\vb{p}}$ is the dipole moment operator.
+Where $$\vb{E}$$ is an [electric field](/know/concept/electric-field/),
+and $$\hat{\vb{p}}$$ is the dipole moment operator.
 From [Rabi oscillation](/know/concept/rabi-oscillation/),
-we know that the time-varying coefficients $c_g$ and $c_e$
+we know that the time-varying coefficients $$c_g$$ and $$c_e$$
 can then be described by:
 
 $$\begin{aligned}
@@ -53,8 +53,8 @@ $$\begin{aligned}
 \end{aligned}$$
 
 We want to rearrange these equations a bit.
-Therefore, we split the electric field $\vb{E}$ like so,
-where the amplitudes $\vb{E}_0^{-}$ and $\vb{E}_0^{+}$ may be slowly varying:
+Therefore, we split the electric field $$\vb{E}$$ like so,
+where the amplitudes $$\vb{E}_0^{-}$$ and $$\vb{E}_0^{+}$$ may be slowly varying:
 
 $$\begin{aligned}
     \vb{E}(t)
@@ -62,8 +62,8 @@ $$\begin{aligned}
     = \vb{E}_0^{-} \exp(i \omega t) + \vb{E}_0^{+} \exp(-i \omega t)
 \end{aligned}$$
 
-Since $\vb{E}$ is real, $\vb{E}_0^{+} = (\vb{E}_0^{-})^*$.
-Similarly, we define the transition dipole moment $\vb{p}_0^{-}$:
+Since $$\vb{E}$$ is real, $$\vb{E}_0^{+} = (\vb{E}_0^{-})^*$$.
+Similarly, we define the transition dipole moment $$\vb{p}_0^{-}$$:
 
 $$\begin{aligned}
     \vb{p}_0^{-}
@@ -74,8 +74,8 @@ $$\begin{aligned}
     = q \matrixel{g}{\vu{x}}{e}
 \end{aligned}$$
 
-With these, the equations for $c_g$ and $c_e$ can be rewritten as shown below.
-Note that $\vb{E}^{-}$ and $\vb{E}^{+}$ include the driving plane wave, and the
+With these, the equations for $$c_g$$ and $$c_e$$ can be rewritten as shown below.
+Note that $$\vb{E}^{-}$$ and $$\vb{E}^{+}$$ include the driving plane wave, and the
 [rotating wave approximation](/know/concept/rotating-wave-approximation/) is still made:
 
 $$\begin{aligned}
@@ -89,9 +89,9 @@ $$\begin{aligned}
 
 ## Optical Bloch equations
 
-For $\Ket{\Psi}$ as defined above,
+For $$\Ket{\Psi}$$ as defined above,
 the corresponding pure [density operator](/know/concept/density-operator/)
-$\hat{\rho}$ is as follows:
+$$\hat{\rho}$$ is as follows:
 
 $$\begin{aligned}
     \hat{\rho}
@@ -108,9 +108,9 @@ $$\begin{aligned}
     \end{bmatrix}
 \end{aligned}$$
 
-Where $\omega_0 \equiv (E_e \!-\! E_g) / \hbar$ is the resonance frequency.
-We take the $t$-derivative of the matrix elements,
-and insert the equations for $c_g$ and $c_e$:
+Where $$\omega_0 \equiv (E_e \!-\! E_g) / \hbar$$ is the resonance frequency.
+We take the $$t$$-derivative of the matrix elements,
+and insert the equations for $$c_g$$ and $$c_e$$:
 
 $$\begin{aligned}
     \dv{\rho_{gg}}{t}
@@ -157,12 +157,12 @@ $$\begin{aligned}
     &= - i \omega_0 \rho_{eg} + \frac{i}{\hbar} \vb{p}_0^{-} \cdot \vb{E}^{+} \big( \rho_{gg} - \rho_{ee} \big)
 \end{aligned}$$
 
-These equations are correct if nothing else is affecting $\hat{\rho}$.
+These equations are correct if nothing else is affecting $$\hat{\rho}$$.
 But in practice, these quantities decay due to various processes,
 e.g. spontaneous emission (see [Einstein coefficients](/know/concept/einstein-coefficients/)).
 
-Let $\rho_{ee}$ decays with rate $\gamma_e$.
-Since the total probability $\rho_{ee} + \rho_{gg} = 1$,
+Let $$\rho_{ee}$$ decays with rate $$\gamma_e$$.
+Since the total probability $$\rho_{ee} + \rho_{gg} = 1$$,
 we thus have:
 
 $$\begin{aligned}
@@ -174,7 +174,7 @@ $$\begin{aligned}
 \end{aligned}$$
 
 Meanwhile, for whatever reason,
-let $\rho_{gg}$ decay into $\rho_{ee}$ with rate $\gamma_g$:
+let $$\rho_{gg}$$ decay into $$\rho_{ee}$$ with rate $$\gamma_g$$:
 
 $$\begin{aligned}
     \Big( \dv{\rho_{gg}}{t} \Big)_{g}
@@ -185,7 +185,7 @@ $$\begin{aligned}
 \end{aligned}$$
 
 And finally, let the diagonal (perpendicular) matrix elements
-both decay with rate $\gamma_\perp$:
+both decay with rate $$\gamma_\perp$$:
 
 $$\begin{aligned}
     \Big( \dv{\rho_{eg}}{t} \Big)_{\perp}
@@ -196,7 +196,7 @@ $$\begin{aligned}
 \end{aligned}$$
 
 Putting everything together,
-we arrive at the **optical Bloch equations** governing $\hat{\rho}$:
+we arrive at the **optical Bloch equations** governing $$\hat{\rho}$$:
 
 $$\begin{aligned}
     \boxed{
@@ -221,12 +221,12 @@ $$\begin{aligned}
 \end{aligned}$$
 
 Many authors simplify these equations a bit by choosing
-$\gamma_g = 0$ and $\gamma_\perp = \gamma_e / 2$.
+$$\gamma_g = 0$$ and $$\gamma_\perp = \gamma_e / 2$$.
 
 
 ## Including Maxwell's equations
 
-This two-level system has a dipole moment $\vb{p}$ as follows,
+This two-level system has a dipole moment $$\vb{p}$$ as follows,
 where we use [Laporte's selection rule](/know/concept/selection-rules/)
 to remove diagonal terms, by assuming that
 the electron's orbitals are odd or even:
@@ -243,8 +243,8 @@ $$\begin{aligned}
     \equiv \vb{p}^{-}(t) + \vb{p}^{+}(t)
 \end{aligned}$$
 
-Where we have split $\vb{p}$ analogously to $\vb{E}$
-by defining $\vb{p}^{+} \equiv \vb{p}_0^{+} \rho_{eg}$.
+Where we have split $$\vb{p}$$ analogously to $$\vb{E}$$
+by defining $$\vb{p}^{+} \equiv \vb{p}_0^{+} \rho_{eg}$$.
 Its equation of motion can then be found from the optical Bloch equations:
 
 $$\begin{aligned}
@@ -254,7 +254,7 @@ $$\begin{aligned}
     + \frac{i}{\hbar} \vb{p}_0^{+} \Big( \vb{p}_0^{-} \cdot \vb{E}^{+} \Big) \Big( \rho_{gg} - \rho_{ee} \Big)
 \end{aligned}$$
 
-Some authors do not bother multiplying $\rho_{ge}$ by $\vb{p}_0^{+}$.
+Some authors do not bother multiplying $$\rho_{ge}$$ by $$\vb{p}_0^{+}$$.
 In any case, we arrive at:
 
 $$\begin{aligned}
@@ -265,7 +265,7 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-Where we have defined the **population inversion** $d \in [-1, 1]$ as follows,
+Where we have defined the **population inversion** $$d \in [-1, 1]$$ as follows,
 which quantifies the electron's excitedness:
 
 $$\begin{aligned}
@@ -285,8 +285,8 @@ $$\begin{aligned}
 
 We can rewrite the first two terms in the following intuitive form,
 which describes a decay with
-rate $\gamma_\parallel \equiv \gamma_g + \gamma_e$
-towards an equilbrium $d_0$:
+rate $$\gamma_\parallel \equiv \gamma_g + \gamma_e$$
+towards an equilbrium $$d_0$$:
 
 $$\begin{aligned}
     2 \gamma_g \rho_{gg} - 2 \gamma_e \rho_{ee}
@@ -313,8 +313,8 @@ $$\begin{aligned}
     + \gamma_g (\rho_{gg} - \rho_{ee}) + \gamma_e (\rho_{gg} - \rho_{ee})
 \end{aligned}$$
 
-Since the total probability $\rho_{gg} + \rho_{ee} = 1$,
-and $d \equiv \rho_{ee} - \rho_{gg}$, this reduces to:
+Since the total probability $$\rho_{gg} + \rho_{ee} = 1$$,
+and $$d \equiv \rho_{ee} - \rho_{gg}$$, this reduces to:
 
 $$\begin{aligned}
     2 \gamma_g \rho_{gg} - 2 \gamma_e \rho_{ee}
@@ -324,10 +324,11 @@ $$\begin{aligned}
     \\
     &= \gamma_\parallel ( d_0 - d )
 \end{aligned}$$
+
 </div>
 </div>
 
-With this, the equation for the population inversion $d$
+With this, the equation for the population inversion $$d$$
 takes the following final form:
 
 $$\begin{aligned}
@@ -338,10 +339,10 @@ $$\begin{aligned}
 \end{aligned}$$
 
 Finally, we would like a relation between the polarization
-and the electric field $\vb{E}$,
+and the electric field $$\vb{E}$$,
 for which we turn to [Maxwell's equations](/know/concept/maxwells-equations/).
 We start from Faraday's law,
-and split $\vb{B} = \mu_0 (\vb{H} + \vb{M})$:
+and split $$\vb{B} = \mu_0 (\vb{H} + \vb{M})$$:
 
 $$\begin{aligned}
     \nabla \cross \vb{E}
@@ -349,9 +350,9 @@ $$\begin{aligned}
     = - \mu_0 \pdv{\vb{H}}{t} - \mu_0 \pdv{\vb{M}}{t}
 \end{aligned}$$
 
-We assume that there is no magnetization $\vb{M} = 0$.
+We assume that there is no magnetization $$\vb{M} = 0$$.
 Then we we take the curl of both sides,
-and replace $\nabla \cross \vb{H}$ with Ampère's circuital law:
+and replace $$\nabla \cross \vb{H}$$ with Ampère's circuital law:
 
 $$\begin{aligned}
     \nabla \cross \big( \nabla \cross \vb{E} \big)
@@ -359,23 +360,23 @@ $$\begin{aligned}
     = - \mu_0 \pdv{}{t} \Big( \vb{J}_\mathrm{free} + \pdv{\vb{D}}{t} \Big)
 \end{aligned}$$
 
-Inserting the definition $\vb{D} = \varepsilon_0 \vb{E} + \vb{P}$
-together with Ohm's law $\vb{J}_\mathrm{free} = \sigma \vb{E}$ yields:
+Inserting the definition $$\vb{D} = \varepsilon_0 \vb{E} + \vb{P}$$
+together with Ohm's law $$\vb{J}_\mathrm{free} = \sigma \vb{E}$$ yields:
 
 $$\begin{aligned}
     \nabla \cross \big( \nabla \cross \vb{E} \big)
     = - \mu_0 \sigma \pdv{\vb{E}}{t} - \mu_0 \varepsilon_0 \pdvn{2}{\vb{E}}{t} - \mu_0 \pdvn{2}{\vb{P}}{t}
 \end{aligned}$$
 
-Where $\sigma$ is the active material's conductivity, if any;
-almost all authors assume $\sigma = 0$.
+Where $$\sigma$$ is the active material's conductivity, if any;
+almost all authors assume $$\sigma = 0$$.
 
 Recall that we are describing the dynamics of a two-level system.
 In reality, such a system (e.g. a quantum dot)
 is suspended in a passive background medium,
-which reacts with a polarization $\vb{P}_\mathrm{med}$
-to the electric field $\vb{E}$.
-If the medium is linear, i.e. $\vb{P}_\mathrm{med} = \varepsilon_0 \chi \vb{E}$,
+which reacts with a polarization $$\vb{P}_\mathrm{med}$$
+to the electric field $$\vb{E}$$.
+If the medium is linear, i.e. $$\vb{P}_\mathrm{med} = \varepsilon_0 \chi \vb{E}$$,
 then:
 
 $$\begin{aligned}
@@ -390,10 +391,10 @@ $$\begin{aligned}
     - \mu_0 \varepsilon_0 \varepsilon_r \pdvn{2}{\vb{E}}{t}
 \end{aligned}$$
 
-Where $\varepsilon_r \equiv 1 + \chi_e$ is the medium's relative permittivity.
-The speed of light $c^2 = 1 / (\mu_0 \varepsilon_0)$,
-and the refractive index $n^2 = \mu_r \varepsilon_r$,
-where $\mu_r = 1$ due to our assumption that $\vb{M} = 0$, so:
+Where $$\varepsilon_r \equiv 1 + \chi_e$$ is the medium's relative permittivity.
+The speed of light $$c^2 = 1 / (\mu_0 \varepsilon_0)$$,
+and the refractive index $$n^2 = \mu_r \varepsilon_r$$,
+where $$\mu_r = 1$$ due to our assumption that $$\vb{M} = 0$$, so:
 
 $$\begin{aligned}
     \boxed{
@@ -402,9 +403,9 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-$\vb{E}$ and $\vb{P}$ can trivially be replaced by $\vb{E}^{+}$ and $\vb{P}^{+}$.
-It is also simple to convert $\vb{p}^{+}$ and $d$
-into the macroscopic $\vb{P}^{+}$ and total $D$
+$$\vb{E}$$ and $$\vb{P}$$ can trivially be replaced by $$\vb{E}^{+}$$ and $$\vb{P}^{+}$$.
+It is also simple to convert $$\vb{p}^{+}$$ and $$d$$
+into the macroscopic $$\vb{P}^{+}$$ and total $$D$$
 by summing over all two-level systems in the medium:
 
 $$\begin{aligned}