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Display information for equation id:math.1793.13 on revision:1793

* Page found: Drehimpulsdarstellung und Streuphasen (eq math.1793.13)

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Hash: c27affe39264676cef0a7229e450f86b

TeX (original user input):

\frac{1}{r}{{u}_{l}}(r)=\frac{2l+1}{2}\left\{ \frac{1}{ikr}\left[ {{e}^{ikr\xi }}{{P}_{l}}(\xi ) \right]_{-1}^{+1}-\frac{1}{{{\left( ikr \right)}^{2}}}\left[ {{e}^{ikr\xi }}{{P}_{l}}\acute{\ }(\xi ) \right]_{-1}^{+1}+\frac{1}{{{\left( ikr \right)}^{3}}}\left[ {{e}^{ikr\xi }}{{P}_{l}}\acute{\ }\acute{\ }(\xi ) \right]_{-1}^{+1}+... \right\}

TeX (checked):

{\frac {1}{r}}{{u}_{l}}(r)={\frac {2l+1}{2}}\left\{{\frac {1}{ikr}}\left[{{e}^{ikr\xi }}{{P}_{l}}(\xi )\right]_{-1}^{+1}-{\frac {1}{{\left(ikr\right)}^{2}}}\left[{{e}^{ikr\xi }}{{P}_{l}}{\acute {\ }}(\xi )\right]_{-1}^{+1}+{\frac {1}{{\left(ikr\right)}^{3}}}\left[{{e}^{ikr\xi }}{{P}_{l}}{\acute {\ }}{\acute {\ }}(\xi )\right]_{-1}^{+1}+...\right\}

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MathML (3.915 KB / 477 B) :

1rul(r)=2l+12{1ikr[eikrξPl(ξ)]1+11(ikr)2[eikrξPl´(ξ)]1+1+1(ikr)3[eikrξPl´´(ξ)]1+1+...}
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></mfrac></mrow><msub><mi>u</mi><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub><mo stretchy="false">(</mo><mi>r</mi><mo stretchy="false">)</mo><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>l</mi><mo>+</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">{</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>k</mi><mi>r</mi></mrow></mrow></mfrac></mrow><msubsup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>k</mi><mi>r</mi><mi>&#x03BE;</mi></mrow></mrow></msup><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub><mo stretchy="false">(</mo><mi>&#x03BE;</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">]</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>+</mo><mn>1</mn></mrow></mrow></msubsup><mo>&#x2212;</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>i</mi><mi>k</mi><mi>r</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><msubsup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>k</mi><mi>r</mi><mi>&#x03BE;</mi></mrow></mrow></msup><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mi>&#x03BE;</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">]</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>+</mo><mn>1</mn></mrow></mrow></msubsup><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>i</mi><mi>k</mi><mi>r</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow></msup></mrow></mfrac></mrow><msubsup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">[</mo><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mi>k</mi><mi>r</mi><mi>&#x03BE;</mi></mrow></mrow></msup><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mi>l</mi></mrow></msub><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mspace width="0.5em"/><mo data-mjx-pseudoscript="true">´</mo></mover></mrow></mrow><mo stretchy="false">(</mo><mi>&#x03BE;</mi><mo stretchy="false">)</mo><mo data-mjx-texclass="CLOSE">]</mo></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>&#x2212;</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo>+</mo><mn>1</mn></mrow></mrow></msubsup><mo>+</mo><mo>.</mo><mo>.</mo><mo>.</mo><mo data-mjx-texclass="CLOSE">}</mo></mrow></mstyle></mrow></math>

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