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* Page found: Dynamik im Schrödinger- Heisenberg- und Wechselwirkungsbild (eq math.1641.48)

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\frac{d}{dt}{{\hat{F}}_{H}}(t)=\frac{i}{\hbar }\hat{H}{{e}^{\frac{i}{\hbar }\hat{H}t}}{{\hat{F}}_{S}}{{e}^{-\frac{i}{\hbar }\hat{H}t}}+{{e}^{\frac{i}{\hbar }\hat{H}t}}{{\hat{F}}_{S}}\left( -\frac{i}{\hbar }\hat{H} \right){{e}^{-\frac{i}{\hbar }\hat{H}t}}

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d d ⁢ t ⁢ F ^ H ⁢ ( t ) = i ℏ ⁢ H ^ ⁢ e i ℏ ⁢ H ^ ⁢ t ⁢ F ^ S ⁢ e - i ℏ ⁢ H ^ ⁢ t + e i ℏ ⁢ H ^ ⁢ t ⁢ F ^ S ⁢ ( - i ℏ ⁢ H ^ ) ⁢ e - i ℏ ⁢ H ^ ⁢ t 𝑑 𝑑 𝑡 subscript ^ 𝐹 𝐻 𝑡 𝑖 Planck-constant-over-2-pi ^ 𝐻 superscript 𝑒 𝑖 Planck-constant-over-2-pi ^ 𝐻 𝑡 subscript ^ 𝐹 𝑆 superscript 𝑒 𝑖 Planck-constant-over-2-pi ^ 𝐻 𝑡 superscript 𝑒 𝑖 Planck-constant-over-2-pi ^ 𝐻 𝑡 subscript ^ 𝐹 𝑆 𝑖 Planck-constant-over-2-pi ^ 𝐻 superscript 𝑒 𝑖 Planck-constant-over-2-pi ^ 𝐻 𝑡 {\displaystyle{\displaystyle\frac{d}{dt}{{\hat{F}}_{H}}(t)=\frac{i}{\hbar}\hat% {H}{{e}^{\frac{i}{\hbar}\hat{H}t}}{{\hat{F}}_{S}}{{e}^{-\frac{i}{\hbar}\hat{H}% t}}+{{e}^{\frac{i}{\hbar}\hat{H}t}}{{\hat{F}}_{S}}\left(-\frac{i}{\hbar}\hat{H% }\right){{e}^{-\frac{i}{\hbar}\hat{H}t}}}}

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ddtF^H(t)=iℏH^eiℏH^tF^Se−iℏH^t+eiℏH^tF^S(−iℏH^)e−iℏH^t

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Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“