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Display information for equation id:math.1641.12 on revision:1641

* Page found: Dynamik im Schrödinger- Heisenberg- und Wechselwirkungsbild (eq math.1641.12)

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\frac{d}{dt}\left\langle {\hat{F}} \right\rangle =\frac{d}{dt}{{\left\langle  \Psi  \right|}_{t}}\hat{F}{{\left| \Psi  \right\rangle }_{t}}={{\left\langle  \Psi  \right|}_{t}}\frac{\partial \hat{F}}{\partial t}+\frac{i}{\hbar }\left[ \hat{H},\hat{F} \right]{{\left| \Psi  \right\rangle }_{t}}

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d d ⁢ t ⁢ ⟨ F ^ ⟩ = d d ⁢ t ⁢ ⟨ Ψ | t ⁢ F ^ ⁢ | Ψ ⟩ t = ⟨ Ψ | t ⁢ ∂ ⁡ F ^ ∂ ⁡ t + i ℏ ⁢ [ H ^ , F ^ ] ⁢ | Ψ ⟩ t 𝑑 𝑑 𝑡 delimited-⟨⟩ ^ 𝐹 𝑑 𝑑 𝑡 subscript bra Ψ 𝑡 ^ 𝐹 subscript ket Ψ 𝑡 subscript bra Ψ 𝑡 ^ 𝐹 𝑡 𝑖 Planck-constant-over-2-pi ^ 𝐻 ^ 𝐹 subscript ket Ψ 𝑡 {\displaystyle{\displaystyle\frac{d}{dt}\left\langle{\hat{F}}\right\rangle=% \frac{d}{dt}{{\left\langle\Psi\right|}_{t}}\hat{F}{{\left|\Psi\right\rangle}_{% t}}={{\left\langle\Psi\right|}_{t}}\frac{\partial\hat{F}}{\partial t}+\frac{i}% {\hbar}\left[\hat{H},\hat{F}\right]{{\left|\Psi\right\rangle}_{t}}}}

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ddt⟨F^⟩=ddt⟨Ψ|tF^|Ψ⟩t=⟨Ψ|t∂F^∂t+iℏ[H^,F^]|Ψ⟩t

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