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Display information for equation id:math.1677.85 on revision:1677
* Page found: Kugelsymmetrische Potentiale (eq math.1677.85)
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Hash: d25cdd1fa1a1faf6cb7b97dec2dd7571
TeX (original user input):
\int_{{}}^{{}}{{{d}^{3}}r}{{\left| {{\Psi }_{nlm}} \right|}^{2}}=\int_{{}}^{{}}{d\Omega }{{\left| {{Y}_{l}}^{m}(\vartheta ,\phi ) \right|}^{2}}\int_{0}^{\infty }{{{r}^{2}}{{\left| \frac{{{u}_{nl}}(r)}{r} \right|}^{2}}=}\int_{{}}^{{}}{d\Omega }{{\left| {{Y}_{l}}^{m}(\vartheta ,\phi ) \right|}^{2}}\int_{0}^{\infty }{{{\left| {{u}_{nl}}(r) \right|}^{2}}}<\infty
TeX (checked):
\int _{}^{}{{{d}^{3}}r}{{\left|{{\Psi }_{nlm}}\right|}^{2}}=\int _{}^{}{d\Omega }{{\left|{{Y}_{l}}^{m}(\vartheta ,\phi )\right|}^{2}}\int _{0}^{\infty }{{{r}^{2}}{{\left|{\frac {{{u}_{nl}}(r)}{r}}\right|}^{2}}=}\int _{}^{}{d\Omega }{{\left|{{Y}_{l}}^{m}(\vartheta ,\phi )\right|}^{2}}\int _{0}^{\infty }{{\left|{{u}_{nl}}(r)\right|}^{2}}<\infty
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MathML (3.558 KB / 472 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msup><mi>d</mi><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup><mi>r</mi></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><msub><mi mathvariant="normal">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 data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mi mathvariant="normal">Ω</mi></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><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><mo stretchy="false">(</mo><mi>ϑ</mi><mo>,</mo><mi>ϕ</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</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><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo></mrow><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"></mrow><mrow data-mjx-texclass="ORD"></mrow></munderover></mstyle><mrow data-mjx-texclass="ORD"><mi>d</mi><mi mathvariant="normal">Ω</mi></mrow><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><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><mo stretchy="false">(</mo><mi>ϑ</mi><mo>,</mo><mi>ϕ</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mstyle displaystyle="true" scriptlevel="0"><munderover><mo texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">∞</mi></mrow></munderover></mstyle><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><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><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo><</mo><mi mathvariant="normal">∞</mi></mstyle></mrow></math>
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