From f2970c55894b3c8d5fd2926a8918d166988109fe Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Fri, 12 Nov 2021 20:20:05 +0100
Subject: Expand knowledge base

---
 content/know/concept/heisenberg-picture/index.pdc | 8 ++++++--
 1 file changed, 6 insertions(+), 2 deletions(-)

(limited to 'content/know/concept/heisenberg-picture/index.pdc')

diff --git a/content/know/concept/heisenberg-picture/index.pdc b/content/know/concept/heisenberg-picture/index.pdc
index c49169f..03a386d 100644
--- a/content/know/concept/heisenberg-picture/index.pdc
+++ b/content/know/concept/heisenberg-picture/index.pdc
@@ -19,11 +19,15 @@ mechanics, and is equivalent to the traditionally-taught Schrödinger equation.
 In the Schrödinger picture, the operators (observables) are fixed
 (as long as they do not depend on time), while the state
 $\ket{\psi_S(t)}$ changes according to the Schrödinger equation,
-which can be written using the generator of translations
-$\hat{U}(t) = \exp\!(- i t \hat{H} / \hbar)$ like so:
+which can be written using the generator of translations $\hat{U}(t)$ like so,
+for a time-independent $\hat{H}_S$:
 
 $$\begin{aligned}
     \ket{\psi_S(t)} = \hat{U}(t) \ket{\psi_S(0)}
+    \qquad \quad
+    \boxed{
+        \hat{U}(t) \equiv \exp\!\bigg(\!-\! i \frac{\hat{H}_S t}{\hbar} \bigg)
+    }
 \end{aligned}$$
 
 In contrast, the Heisenberg picture reverses the roles:
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