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Display information for equation id:math.2709.157 on revision:2709

* Page found: Formaler Aufbau der Quantenmechanik (eq math.2709.157)

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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{matrix} 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{matrix}

<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mtable displaystyle="true"><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>χ</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mo stretchy="false">=</mo><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msub><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>ω</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>Ω</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>t</mi></mrow></mrow></msup><mo stretchy="false">+</mo><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">−</mo></mrow></msub><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>ω</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo stretchy="false">−</mo><mspace width="0.167em"></mspace><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>Ω</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>t</mi></mrow></mrow></msup><mspace width="1em"></mspace><msub><mi>c</mi><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">±</mo></mrow></msub><mo stretchy="false">∈</mo><mrow data-mjx-texclass="ORD"><mi>ℂ</mi></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo stretchy="false">=</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>𝔦</mi></mrow><mi>ω</mi><mi>t</mi></mrow></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mi>α</mi><mi>cos</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>Ω</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo stretchy="false">+</mo><mi>β</mi><mi>sin</mi><mo>&#x2061;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msub><mi>Ω</mi><mrow data-mjx-texclass="ORD"><mi>R</mi></mrow></msub></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">}</mo></mrow><mspace width="1em"></mspace><mi>α</mi><mo>,</mo><mi>β</mi><mo stretchy="false">∈</mo><mrow data-mjx-texclass="ORD"><mi>ℂ</mi></mrow></mtd></mtr></mtable></mstyle></mrow></math>

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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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