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/hellmann-feynman-theorem/index.md | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

(limited to 'source/know/concept/hellmann-feynman-theorem')

diff --git a/source/know/concept/hellmann-feynman-theorem/index.md b/source/know/concept/hellmann-feynman-theorem/index.md
index 9ffff34..e18acc2 100644
--- a/source/know/concept/hellmann-feynman-theorem/index.md
+++ b/source/know/concept/hellmann-feynman-theorem/index.md
@@ -9,7 +9,7 @@ layout: "concept"
 ---
 
 Consider the time-independent Schrödinger equation,
-where the Hamiltonian $\hat{H}$ depends on a general parameter $\lambda$,
+where the Hamiltonian $$\hat{H}$$ depends on a general parameter $$\lambda$$,
 whose meaning or type we will not specify:
 
 $$\begin{aligned}
@@ -17,7 +17,7 @@ $$\begin{aligned}
     = E_n(\lambda) \Ket{\psi_n(\lambda)}
 \end{aligned}$$
 
-Assuming all eigenstates $\Ket{\psi_n}$ are normalized,
+Assuming all eigenstates $$\Ket{\psi_n}$$ are normalized,
 this gives us the following basic relation:
 
 $$\begin{aligned}
@@ -26,7 +26,7 @@ $$\begin{aligned}
     = \delta_{mn} E_n
 \end{aligned}$$
 
-We differentiate this with respect to $\lambda$,
+We differentiate this with respect to $$\lambda$$,
 which could be a scalar or a vector.
 This yields:
 
@@ -43,9 +43,9 @@ $$\begin{aligned}
 
 In order to simplify this,
 we differentiate the orthogonality relation
-$\Inprod{\psi_m}{\psi_n} = \delta_{mn}$,
+$$\Inprod{\psi_m}{\psi_n} = \delta_{mn}$$,
 which ends up telling us that
-$\Inprod{\nabla_\lambda \psi_m}{\psi_n} = - \Inprod{\psi_m}{\nabla_\lambda \psi_n}$:
+$$\Inprod{\nabla_\lambda \psi_m}{\psi_n} = - \Inprod{\psi_m}{\nabla_\lambda \psi_n}$$:
 
 $$\begin{aligned}
     0
@@ -54,7 +54,7 @@ $$\begin{aligned}
     = \Inprod{\nabla_\lambda \psi_m}{\psi_n} + \Inprod{\psi_m}{\nabla_\lambda \psi_n}
 \end{aligned}$$
 
-Using this result to replace $\Inprod{\nabla_\lambda \psi_m}{\psi_n}$
+Using this result to replace $$\Inprod{\nabla_\lambda \psi_m}{\psi_n}$$
 in the previous equation leads to:
 
 $$\begin{aligned}
@@ -62,9 +62,9 @@ $$\begin{aligned}
     &= (E_m - E_n) \Inprod{\psi_m}{\nabla_\lambda \psi_n} + \matrixel{\psi_m}{\nabla_\lambda \hat{H}}{\psi_n}
 \end{aligned}$$
 
-For $m = n$, we therefore arrive at the **Hellmann-Feynman theorem**,
+For $$m = n$$, we therefore arrive at the **Hellmann-Feynman theorem**,
 which is useful when doing numerical calculations
-to minimize energies with respect to $\lambda$:
+to minimize energies with respect to $$\lambda$$:
 
 $$\begin{aligned}
     \boxed{
@@ -73,7 +73,7 @@ $$\begin{aligned}
     }
 \end{aligned}$$
 
-While for $m \neq n$, we get the **Epstein generalization**
+While for $$m \neq n$$, we get the **Epstein generalization**
 of the Hellmann-Feynman theorem, which is for example relevant for
 the [Berry phase](/know/concept/berry-phase/):
 
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