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Display information for equation id:math.1649.61 on revision:1649
* Page found: Dynamik im Schrödinger- Heisenberg- und Wechselwirkungsbild (eq math.1649.61)
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TeX (original user input):
\begin{align}
& \left\langle {{{\hat{F}}}_{S}} \right\rangle ={{\left\langle \Psi \right|}_{t}}{{{\hat{F}}}_{S}}{{\left| \Psi \right\rangle }_{t}}={{\left\langle \Psi \right|}_{t}}{{e}^{-\frac{i}{\hbar }{{{\hat{H}}}^{0}}t}}{{e}^{+\frac{i}{\hbar }{{{\hat{H}}}^{0}}t}}{{{\hat{F}}}_{S}}{{e}^{-\frac{i}{\hbar }{{{\hat{H}}}^{0}}t}}{{e}^{+\frac{i}{\hbar }{{{\hat{H}}}^{0}}t}}{{\left| \Psi \right\rangle }_{t}} \\
& {{\left\langle \Psi \right|}_{t}}{{e}^{-\frac{i}{\hbar }{{{\hat{H}}}^{0}}t}}={{\left\langle \Psi \right|}_{W}} \\
& {{e}^{+\frac{i}{\hbar }{{{\hat{H}}}^{0}}t}}{{{\hat{F}}}_{S}}{{e}^{-\frac{i}{\hbar }{{{\hat{H}}}^{0}}t}}={{{\hat{F}}}_{W}}(t) \\
& {{e}^{+\frac{i}{\hbar }{{{\hat{H}}}^{0}}t}}{{\left| \Psi \right\rangle }_{0}}={{\left| \Psi \right\rangle }_{W}} \\
& \left\langle {{{\hat{F}}}_{S}} \right\rangle ={{\left\langle \Psi \right|}_{W}}{{{\hat{F}}}_{W}}(t){{\left| \Psi \right\rangle }_{W}} \\
\end{align}
TeX (checked):
{\begin{aligned}&\left\langle {{\hat {F}}_{S}}\right\rangle ={{\left\langle \Psi \right|}_{t}}{{\hat {F}}_{S}}{{\left|\Psi \right\rangle }_{t}}={{\left\langle \Psi \right|}_{t}}{{e}^{-{\frac {i}{\hbar }}{{\hat {H}}^{0}}t}}{{e}^{+{\frac {i}{\hbar }}{{\hat {H}}^{0}}t}}{{\hat {F}}_{S}}{{e}^{-{\frac {i}{\hbar }}{{\hat {H}}^{0}}t}}{{e}^{+{\frac {i}{\hbar }}{{\hat {H}}^{0}}t}}{{\left|\Psi \right\rangle }_{t}}\\&{{\left\langle \Psi \right|}_{t}}{{e}^{-{\frac {i}{\hbar }}{{\hat {H}}^{0}}t}}={{\left\langle \Psi \right|}_{W}}\\&{{e}^{+{\frac {i}{\hbar }}{{\hat {H}}^{0}}t}}{{\hat {F}}_{S}}{{e}^{-{\frac {i}{\hbar }}{{\hat {H}}^{0}}t}}={{\hat {F}}_{W}}(t)\\&{{e}^{+{\frac {i}{\hbar }}{{\hat {H}}^{0}}t}}{{\left|\Psi \right\rangle }_{0}}={{\left|\Psi \right\rangle }_{W}}\\&\left\langle {{\hat {F}}_{S}}\right\rangle ={{\left\langle \Psi \right|}_{W}}{{\hat {F}}_{W}}(t){{\left|\Psi \right\rangle }_{W}}\\\end{aligned}}
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