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Display information for equation id:math.1734.27 on revision:1734
* Page found: Induzierte Emission und Absorption von Lichtquanten in Atomen (eq math.1734.27)
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\begin{align}
& {{\Psi }_{nlm}}(\bar{r})=\frac{{{u}_{nl}}(r)}{r}{{Y}_{l}}^{m}\left( \vartheta ,\phi \right)\tilde{\ }{{P}_{l}}^{m}(\cos \vartheta ){{e}^{im\phi }} \\
& \left\langle n\acute{\ }l\acute{\ }m\acute{\ } \right|\hat{\bar{\xi }}\left| nlm \right\rangle \tilde{\ }\int_{0}^{\pi }{d}\vartheta {{\sin }^{2}}\left( \vartheta \right){{P}_{l\acute{\ }}}^{m\acute{\ }}(\cos \vartheta ){{P}_{l}}^{m}(\cos \vartheta )\int_{0}^{2\pi }{d}\phi {{e}^{i\left( m-m\acute{\ }+1 \right)\phi }} \\
& \int_{0}^{2\pi }{d}\phi {{e}^{i\left( m-m\acute{\ }+1 \right)\phi }}\tilde{\ }{{\delta }_{m\acute{\ },m+1}} \\
& \Rightarrow \left\langle n\acute{\ }l\acute{\ }m\acute{\ } \right|\hat{\bar{\xi }}\left| nlm \right\rangle \tilde{\ }\int_{0}^{\pi }{d}\vartheta {{\sin }^{2}}\left( \vartheta \right){{P}_{l\acute{\ }}}^{m+1}(\cos \vartheta ){{P}_{l}}^{m}(\cos \vartheta ) \\
& \int_{0}^{\pi }{d}\vartheta {{\sin }^{2}}\left( \vartheta \right){{P}_{l\acute{\ }}}^{m+1}(\cos \vartheta ){{P}_{l}}^{m}(\cos \vartheta )\tilde{\ }{{\delta }_{l\acute{\ },l\pm 1}} \\
& \Rightarrow \left\langle n\acute{\ }l\acute{\ }m\acute{\ } \right|\hat{\bar{\xi }}\left| nlm \right\rangle \tilde{\ }{{\delta }_{m\acute{\ },m+1}}{{\delta }_{l\acute{\ },l\pm 1}} \\
\end{align}
TeX (checked):
{\begin{aligned}&{{\Psi }_{nlm}}({\bar {r}})={\frac {{{u}_{nl}}(r)}{r}}{{Y}_{l}}^{m}\left(\vartheta ,\phi \right){\tilde {\ }}{{P}_{l}}^{m}(\cos \vartheta ){{e}^{im\phi }}\\&\left\langle n{\acute {\ }}l{\acute {\ }}m{\acute {\ }}\right|{\hat {\bar {\xi }}}\left|nlm\right\rangle {\tilde {\ }}\int _{0}^{\pi }{d}\vartheta {{\sin }^{2}}\left(\vartheta \right){{P}_{l{\acute {\ }}}}^{m{\acute {\ }}}(\cos \vartheta ){{P}_{l}}^{m}(\cos \vartheta )\int _{0}^{2\pi }{d}\phi {{e}^{i\left(m-m{\acute {\ }}+1\right)\phi }}\\&\int _{0}^{2\pi }{d}\phi {{e}^{i\left(m-m{\acute {\ }}+1\right)\phi }}{\tilde {\ }}{{\delta }_{m{\acute {\ }},m+1}}\\&\Rightarrow \left\langle n{\acute {\ }}l{\acute {\ }}m{\acute {\ }}\right|{\hat {\bar {\xi }}}\left|nlm\right\rangle {\tilde {\ }}\int _{0}^{\pi }{d}\vartheta {{\sin }^{2}}\left(\vartheta \right){{P}_{l{\acute {\ }}}}^{m+1}(\cos \vartheta ){{P}_{l}}^{m}(\cos \vartheta )\\&\int _{0}^{\pi }{d}\vartheta {{\sin }^{2}}\left(\vartheta \right){{P}_{l{\acute {\ }}}}^{m+1}(\cos \vartheta ){{P}_{l}}^{m}(\cos \vartheta ){\tilde {\ }}{{\delta }_{l{\acute {\ }},l\pm 1}}\\&\Rightarrow \left\langle n{\acute {\ }}l{\acute {\ }}m{\acute {\ }}\right|{\hat {\bar {\xi }}}\left|nlm\right\rangle {\tilde {\ }}{{\delta }_{m{\acute {\ }},m+1}}{{\delta }_{l{\acute {\ }},l\pm 1}}\\\end{aligned}}
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<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>Ψ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mi>l</mi><mi>m</mi></mrow></mrow></msub><mo stretchy="false">(</mo><mover><mi>r</mi><mo>¯</mo></mover><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mi>l</mi></mrow></mrow></msub><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></mfrac></mrow><msup><msub><mi>Y</mi><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ϑ</mi><mo>,</mo><mi>ϕ</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mover><mtext> </mtext><mo>~</mo></mover><msup><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msup><mo stretchy="false">(</mo><mi>cos</mi><mo>⁡</mo><mi>ϑ</mi><mo stretchy="false">)</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>m</mi><mi>ϕ</mi></mrow></mrow></msup></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>n</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>l</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mi>m</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover><mo 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data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>l</mi><mover><mtext> </mtext><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>m</mi><mo stretchy="false">+</mo><mn>1</mn></mrow></mrow></msup><mo stretchy="false">(</mo><mi>cos</mi><mo>⁡</mo><mi>ϑ</mi><mo stretchy="false">)</mo><msup><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mi>m</mi></mrow></msup><mo stretchy="false">(</mo><mi>cos</mi><mo>⁡</mo><mi>ϑ</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msubsup><mo stretchy="false">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi>π</mi></mrow></msubsup><mi>d</mi><mi>ϑ</mi><msup><mi>sin</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>ϑ</mi><mo 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