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authorPrefetch2021-11-12 20:20:05 +0100
committerPrefetch2021-11-12 20:20:05 +0100
commitf2970c55894b3c8d5fd2926a8918d166988109fe (patch)
treebe07d30a501b84cc3e6a80f70c6f5a729f6b28dc /content/know/concept/heisenberg-picture/index.pdc
parent2a91bdedf299a7fa7b513785d51a63e2f147f37f (diff)
Expand knowledge base
Diffstat (limited to 'content/know/concept/heisenberg-picture/index.pdc')
-rw-r--r--content/know/concept/heisenberg-picture/index.pdc8
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diff --git a/content/know/concept/heisenberg-picture/index.pdc b/content/know/concept/heisenberg-picture/index.pdc
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--- 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: