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Display information for equation id:math.1734.25 on revision:1734
* Page found: Induzierte Emission und Absorption von Lichtquanten in Atomen (eq math.1734.25)
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Hash: 12918be1216f6e2865d5f623afc78c62
TeX (original user input):
\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 }} \\
& {{x}_{1}}=r\sin \vartheta \cos \phi \\
& {{x}_{2}}=r\sin \vartheta \sin \phi \\
& {{x}_{3}}=r\cos \vartheta \\
\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 }}\\&{{x}_{1}}=r\sin \vartheta \cos \phi \\&{{x}_{2}}=r\sin \vartheta \sin \phi \\&{{x}_{3}}=r\cos \vartheta \\\end{aligned}}
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MathML (2.397 KB / 486 B) :
<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"><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">=</mo><mi>r</mi><mi>sin</mi><mo>⁡</mo><mi>ϑ</mi><mi>cos</mi><mo>⁡</mo><mi>ϕ</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msub><mo stretchy="false">=</mo><mi>r</mi><mi>sin</mi><mo>⁡</mo><mi>ϑ</mi><mi>sin</mi><mo>⁡</mo><mi>ϕ</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mi>x</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msub><mo stretchy="false">=</mo><mi>r</mi><mi>cos</mi><mo>⁡</mo><mi>ϑ</mi></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd></mtr></mtable></mstyle></mrow></math>
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