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authorPrefetch2023-04-02 16:57:12 +0200
committerPrefetch2023-04-02 16:57:12 +0200
commita8d31faecc733fa4d63fde58ab98a5e9d11029c2 (patch)
treeb8d039b13e026fb68f0bed439a2cb73397c35981 /source/know/concept/amplitude-rate-equations
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Improve knowledge base
Diffstat (limited to 'source/know/concept/amplitude-rate-equations')
-rw-r--r--source/know/concept/amplitude-rate-equations/index.md20
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diff --git a/source/know/concept/amplitude-rate-equations/index.md b/source/know/concept/amplitude-rate-equations/index.md
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--- a/source/know/concept/amplitude-rate-equations/index.md
+++ b/source/know/concept/amplitude-rate-equations/index.md
@@ -9,21 +9,17 @@ layout: "concept"
---
In quantum mechanics, the **amplitude rate equations** give
-the evolution of a quantum state's superposition coefficients through time.
-They are known as the precursors for
+the evolution of a quantum state in a time-varying potential.
+Although best known as the precursors of
[time-dependent perturbation theory](/know/concept/time-dependent-perturbation-theory/),
-but by themselves they are exact and widely applicable.
+by themselves they are exact and widely applicable.
-Let $$\hat{H}_0$$ be a "simple" time-independent part
-of the full Hamiltonian,
-and $$\hat{H}_1$$ a time-varying other part,
-whose contribution need not be small:
+Let $$\hat{H}_0$$ be the time-independent part of the total Hamiltonian,
+and $$\hat{H}_1$$ the time-varying part
+(whose contribution need not be small),
+so $$\hat{H}(t) = \hat{H}_0 + \hat{H}_1(t)$$.
-$$\begin{aligned}
- \hat{H}(t) = \hat{H}_0 + \hat{H}_1(t)
-\end{aligned}$$
-
-We assume that the time-independent problem
+Suppose that the time-independent problem
$$\hat{H}_0 \Ket{n} = E_n \Ket{n}$$ has already been solved,
such that its general solution is a superposition as follows: