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Diffstat (limited to 'content/know/concept/heisenberg-picture')
| -rw-r--r-- | content/know/concept/heisenberg-picture/index.pdc | 8 |
1 files changed, 6 insertions, 2 deletions
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: |