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Display information for equation id:math.1702.34 on revision:1702

* Page found: Zustände mit Bahn- und Spinvariablen (eq math.1702.34)

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Hash: 4ee9d8c45e130c51fc6a6e1ed818d035

TeX (original user input):

\begin{align}
& \left( \begin{matrix}

{{{\hat{H}}}_{\acute{\ }B}}+\hbar {{\omega }_{l}} & 0 \\
0 & {{{\hat{H}}}_{\acute{\ }B}}-\hbar {{\omega }_{l}} \\
\end{matrix} \right)\left( \begin{matrix}

{{\left| {{\Psi }_{1}} \right\rangle }_{t}} \\

{{\left| {{\Psi }_{2}} \right\rangle }_{t}} \\
\end{matrix} \right)=i\hbar \frac{\partial }{\partial t}\left( \begin{matrix}

{{\left| {{\Psi }_{1}} \right\rangle }_{t}} \\

{{\left| {{\Psi }_{2}} \right\rangle }_{t}} \\
\end{matrix} \right) \\
& \Leftrightarrow \left( {{{\hat{H}}}_{\acute{\ }B}}+\hbar {{\omega }_{l}} \right){{\left| {{\Psi }_{1}} \right\rangle }_{t}}=i\hbar \frac{\partial }{\partial t}{{\left| {{\Psi }_{1}} \right\rangle }_{t}} \\
& \left( {{{\hat{H}}}_{\acute{\ }B}}-\hbar {{\omega }_{l}} \right){{\left| {{\Psi }_{2}} \right\rangle }_{t}}=i\hbar \frac{\partial }{\partial t}{{\left| {{\Psi }_{2}} \right\rangle }_{t}} \\
\end{align}

TeX (checked):

{\begin{aligned}&\left({\begin{matrix}{{\hat {H}}_{{\acute {\ }}B}}+\hbar {{\omega }_{l}}&0\\0&{{\hat {H}}_{{\acute {\ }}B}}-\hbar {{\omega }_{l}}\\\end{matrix}}\right)\left({\begin{matrix}{{\left|{{\Psi }_{1}}\right\rangle }_{t}}\\{{\left|{{\Psi }_{2}}\right\rangle }_{t}}\\\end{matrix}}\right)=i\hbar {\frac {\partial }{\partial t}}\left({\begin{matrix}{{\left|{{\Psi }_{1}}\right\rangle }_{t}}\\{{\left|{{\Psi }_{2}}\right\rangle }_{t}}\\\end{matrix}}\right)\\&\Leftrightarrow \left({{\hat {H}}_{{\acute {\ }}B}}+\hbar {{\omega }_{l}}\right){{\left|{{\Psi }_{1}}\right\rangle }_{t}}=i\hbar {\frac {\partial }{\partial t}}{{\left|{{\Psi }_{1}}\right\rangle }_{t}}\\&\left({{\hat {H}}_{{\acute {\ }}B}}-\hbar {{\omega }_{l}}\right){{\left|{{\Psi }_{2}}\right\rangle }_{t}}=i\hbar {\frac {\partial }{\partial t}}{{\left|{{\Psi }_{2}}\right\rangle }_{t}}\\\end{aligned}}

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\begin{aligned} (\begin{matrix} {\hat{H}}_{\overset{´}{} B} + ℏ ω_{l} & 0 \\ 0 & {\hat{H}}_{\overset{´}{} B} - ℏ ω_{l} \end{matrix}) (\begin{matrix} {| Ψ_{1} ⟩}_{t} \\ {| Ψ_{2} ⟩}_{t} \end{matrix}) = i ℏ \frac{\partial}{\partial t} (\begin{matrix} {| Ψ_{1} ⟩}_{t} \\ {| Ψ_{2} ⟩}_{t} \end{matrix}) \\ \Leftrightarrow ({\hat{H}}_{\overset{´}{} B} + ℏ ω_{l}) {| Ψ_{1} ⟩}_{t} = i ℏ \frac{\partial}{\partial t} {| Ψ_{1} ⟩}_{t} \\ ({\hat{H}}_{\overset{´}{} B} - ℏ ω_{l}) {| Ψ_{2} ⟩}_{t} = i ℏ \frac{\partial}{\partial t} {| Ψ_{2} ⟩}_{t} \end{aligned}

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Identifiers

$\hat{H}$

$\overset{´}{}$

$B$

$ω_{l}$

$\hat{H}$

$\overset{´}{}$

$B$

$ω_{l}$

$Ψ_{1} t$

$Ψ_{2} t$

$i$

$t$

$Ψ_{1} t$

$Ψ_{2} t$

$\hat{H}$

$\overset{´}{}$

$B$

$ω_{l}$

$Ψ_{1} t$

$i$

$t$

$Ψ_{1} t$

$\hat{H}$

$\overset{´}{}$

$B$

$ω_{l}$

$Ψ_{2} t$

$i$

$t$

$Ψ_{2} t$

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