- testwiki

General

Display information for equation id:math.1734.7 on revision:1734

* Page found: Induzierte Emission und Absorption von Lichtquanten in Atomen (eq math.1734.7)

Occurrences on the following pages:

Induzierte Emission und Absorption von Lichtquanten in Atomen Eq: math.1737.7

Hash: 1d6adfbf8410f5cdb3def350df302eaa

TeX (original user input):

\begin{align}

& {{W}_{nn0}}=\frac{2\pi }{\hbar }{{\left| \left\langle  n \right|\hat{F}\left| {{n}_{0}} \right\rangle  \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}-\hbar \omega )+\frac{2\pi }{\hbar }{{\left| \left\langle  {{n}_{0}} \right|{{{\hat{F}}}^{+}}\left| n \right\rangle  \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}+\hbar \omega ) \\
& {{W}_{nn0}}=\frac{2\pi }{\hbar }{{\left( \frac{e}{2m} \right)}^{2}}\left\{ {{\left| \left\langle  n \right|{{e}^{i\bar{k}\bar{r}}}{{{\bar{A}}}_{0}}\hat{\bar{p}}\left| {{n}_{0}} \right\rangle  \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}-\hbar \omega )+{{\left| \left\langle  {{n}_{0}} \right|{{e}^{-i\bar{k}\bar{r}}}{{{\bar{A}}}_{0}}\hat{\bar{p}}\left| n \right\rangle  \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}+\hbar \omega ) \right\} \\
\end{align}

TeX (checked):

{\begin{aligned}&{{W}_{nn0}}={\frac {2\pi }{\hbar }}{{\left|\left\langle n\right|{\hat {F}}\left|{{n}_{0}}\right\rangle \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}-\hbar \omega )+{\frac {2\pi }{\hbar }}{{\left|\left\langle {{n}_{0}}\right|{{\hat {F}}^{+}}\left|n\right\rangle \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}+\hbar \omega )\\&{{W}_{nn0}}={\frac {2\pi }{\hbar }}{{\left({\frac {e}{2m}}\right)}^{2}}\left\{{{\left|\left\langle n\right|{{e}^{i{\bar {k}}{\bar {r}}}}{{\bar {A}}_{0}}{\hat {\bar {p}}}\left|{{n}_{0}}\right\rangle \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}-\hbar \omega )+{{\left|\left\langle {{n}_{0}}\right|{{e}^{-i{\bar {k}}{\bar {r}}}}{{\bar {A}}_{0}}{\hat {\bar {p}}}\left|n\right\rangle \right|}^{2}}\delta ({{E}_{n}}-{{E}_{n0}}+\hbar \omega )\right\}\\\end{aligned}}

LaTeXML (experimental; uses MathML) rendering

MathML (0 B / 8 B) :

SVG image empty. Force Re-Rendering

SVG (0 B / 8 B) :

MathML (experimental; no images) rendering

MathML (6.018 KB / 635 B) :

\begin{matrix} W_{n n 0} = \frac{2 π}{ℏ} {| ⟨ n | \hat{F} | n_{0} ⟩ |}^{2} δ (E_{n} - E_{n 0} - ℏ ω) + \frac{2 π}{ℏ} {| ⟨ n_{0} | {\hat{F}}^{+} | n ⟩ |}^{2} δ (E_{n} - E_{n 0} + ℏ ω) \\ W_{n n 0} = \frac{2 π}{ℏ} {(\frac{e}{2 m})}^{2} {{| ⟨ n | e^{i \bar{k} \bar{r}} {\bar{A}}_{0} \hat{\bar{p}} | n_{0} ⟩ |}^{2} δ (E_{n} - E_{n 0} - ℏ ω) + {| ⟨ n_{0} | e^{- i \bar{k} \bar{r}} {\bar{A}}_{0} \hat{\bar{p}} | n ⟩ |}^{2} δ (E_{n} - E_{n 0} + ℏ ω)} \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>W</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mi>n</mi><mn>0</mn></mrow></mrow></msub><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>π</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi alternate="1">ℏ</mi></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>n</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mover><mi>F</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>δ</mi><mo stretchy="false">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mn>0</mn></mrow></mrow></msub><mo stretchy="false">−</mo><mi alternate="1">ℏ</mi><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>π</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi alternate="1">ℏ</mi></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msup><mover><mi>F</mi><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="ORD"><mo stretchy="false" lspace="0" rspace="0">+</mo></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>n</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>δ</mi><mo stretchy="false">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mn>0</mn></mrow></mrow></msub><mo stretchy="false">+</mo><mi alternate="1">ℏ</mi><mi>ω</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>W</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mi>n</mi><mn>0</mn></mrow></mrow></msub><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>π</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi alternate="1">ℏ</mi></mrow></mfrac></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>e</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>m</mi></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>n</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mover><mi>k</mi><mo>¯</mo></mover><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow></msup><msub><mover><mi>A</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mover><mover><mi>p</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>δ</mi><mo stretchy="false">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mn>0</mn></mrow></mrow></msub><mo stretchy="false">−</mo><mi alternate="1">ℏ</mi><mi>ω</mi><mo stretchy="false">)</mo><mo stretchy="false">+</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><msub><mi>n</mi><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mo data-mjx-texclass="CLOSE">|</mo></mrow><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">−</mo><mi>i</mi><mover><mi>k</mi><mo>¯</mo></mover><mover><mi>r</mi><mo>¯</mo></mover></mrow></mrow></msup><msub><mover><mi>A</mi><mo>¯</mo></mover><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow></msub><mover><mover><mi>p</mi><mo>¯</mo></mover><mo stretchy="false">̂</mo></mover><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>n</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>δ</mi><mo stretchy="false">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mn>0</mn></mrow></mrow></msub><mo stretchy="false">+</mo><mi alternate="1">ℏ</mi><mi>ω</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">}</mo></mrow></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>

Translations to Computer Algebra Systems

Translation to Maple

In Maple:

Translation to Mathematica

In Mathematica:

Identifiers

$W_{n n 0}$

$π$

$n$

$\hat{F}$

$n_{0}$

$δ$

$E_{n}$

$E_{n 0}$

$ω$

$π$

$n_{0}$

$\hat{F}$

$n$

$δ$

$E_{n}$

$E_{n 0}$

$ω$

$W_{n n 0}$

$π$

$e$

$m$

$n$

$e$

$i$

$\bar{k}$

$\bar{r}$

${\bar{A}}_{0}$

$\hat{\bar{p}}$

$n_{0}$

$δ$

$E_{n}$

$E_{n 0}$

$ω$

$n_{0}$

$e$

$i$

$\bar{k}$

$\bar{r}$

${\bar{A}}_{0}$

$\hat{\bar{p}}$

$n$

$δ$

$E_{n}$

$E_{n 0}$

$ω$

MathML observations

0results

no statistics present please run the maintenance script ExtractFeatures.php

0 results

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

General

LaTeXML (experimental; uses MathML) rendering

MathML (experimental; no images) rendering

Translations to Computer Algebra Systems

Translation to Maple

Translation to Mathematica

Similar pages

Identifiers

MathML observations

Navigation menu

Search