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Display information for equation id:math.2711.157 on revision:2711

* Page found: Formaler Aufbau der Quantenmechanik (eq math.2711.157)

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Formaler Aufbau der Quantenmechanik Eq: math.2711.157

Hash: 340865ee6fb1d01f445c0fb1743a00a5

TeX (original user input):

\begin{align}
& {{\chi }_{2}}\left( t \right)={{c}_{+}}{{e}^{\mathfrak{i} \left( \frac{\omega }{2}+\frac{{{\Omega }_{R}}}{2} \right)t}}+{{c}_{-}}{{e}^{\mathfrak{i} \left( \frac{\omega }{2}-\,\frac{{{\Omega }_{R}}}{2} \right)t}}\quad {{c}_{\pm }}\in \mathbb{C} \\
& ={{e}^{\mathfrak{i} \omega t}}\left\{ \alpha \cos \frac{{{\Omega }_{R}}}{2}+\beta \sin \frac{{{\Omega }_{R}}}{2} \right\}\quad \alpha ,\beta \in \mathbb{C}
\end{align}

TeX (checked):

{\begin{aligned}&{{\chi }_{2}}\left(t\right)={{c}_{+}}{{e}^{{\mathfrak {i}}\left({\frac {\omega }{2}}+{\frac {{\Omega }_{R}}{2}}\right)t}}+{{c}_{-}}{{e}^{{\mathfrak {i}}\left({\frac {\omega }{2}}-\,{\frac {{\Omega }_{R}}{2}}\right)t}}\quad {{c}_{\pm }}\in \mathbb {C} \\&={{e}^{{\mathfrak {i}}\omega t}}\left\{\alpha \cos {\frac {{\Omega }_{R}}{2}}+\beta \sin {\frac {{\Omega }_{R}}{2}}\right\}\quad \alpha ,\beta \in \mathbb {C} \end{aligned}}

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\begin{aligned} χ_{2} (t) = c_{+} e^{i (\frac{ω}{2} + \frac{Ω_{R}}{2}) t} + c_{-} e^{i (\frac{ω}{2} - \frac{Ω_{R}}{2}) t} c_{\pm} \in ℂ \\ = e^{i ω t} {α \cos \frac{Ω_{R}}{2} + β \sin \frac{Ω_{R}}{2}} α, β \in ℂ \end{aligned}

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Identifiers

$χ_{2}$

$t$

$c_{+}$

$e$

$i$

$ω$

$Ω_{R}$

$t$

$c_{-}$

$e$

$i$

$ω$

$Ω_{R}$

$t$

$c$

$ℂ$

$e$

$i$

$ω$

$t$

$α$

$Ω_{R}$

$β$

$Ω_{R}$

$α$

$β$

$ℂ$

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