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Diffstat (limited to 'source/know/concept/amplitude-rate-equations')
| -rw-r--r-- | source/know/concept/amplitude-rate-equations/index.md | 20 |
1 files changed, 8 insertions, 12 deletions
diff --git a/source/know/concept/amplitude-rate-equations/index.md b/source/know/concept/amplitude-rate-equations/index.md index 0ca3248..d5eeb0d 100644 --- 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: |