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Display information for equation id:math.3414.6 on revision:3414
* Page found: Das Schalenmodell des Kerns (eq math.3414.6)
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Hash: 7dc4f0bad0910394dafc0a7ef73660fe
TeX (original user input):
\begin{align}
\vec l \vec s= & \frac{1}{2}\left( \vec j^{2}- \vec l^{2}- \vec S^{2}\right)\\
\Rightarrow & \frac{1}{2}\left(j(j-1)-l(l+1)-\frac{3}{4}\right)\\
= & \frac{1}{2}l\quad\text{fuer}\quad j=l+{\frac{1}{2}}\\
= & -\frac{1}{2}(l+1)\quad\text{fuer}\quad j=l+{\frac{1}{2}}\end{align}
TeX (checked):
{\begin{aligned}{\vec {l}}{\vec {s}}=&{\frac {1}{2}}\left({\vec {j}}^{2}-{\vec {l}}^{2}-{\vec {S}}^{2}\right)\\\Rightarrow &{\frac {1}{2}}\left(j(j-1)-l(l+1)-{\frac {3}{4}}\right)\\=&{\frac {1}{2}}l\quad {\text{fuer}}\quad j=l+{\frac {1}{2}}\\=&-{\frac {1}{2}}(l+1)\quad {\text{fuer}}\quad j=l+{\frac {1}{2}}\end{aligned}}
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<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"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>l</mi><mo>→</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>s</mi><mo>→</mo></mover></mrow></mrow><mo>=</mo></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>j</mi><mo>→</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>l</mi><mo>→</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>−</mo><msup><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mover><mi>S</mi><mo>→</mo></mover></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd><mo>⇒</mo></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>j</mi><mo stretchy="false">(</mo><mi>j</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mo>−</mo><mi>l</mi><mo stretchy="false">(</mo><mi>l</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>3</mn></mrow><mrow data-mjx-texclass="ORD"><mn>4</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow></mtd></mtr><mtr><mtd><mo>=</mo></mtd><mtd><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mi>l</mi><mspace width="1em"></mspace><mrow data-mjx-texclass="ORD"><mtext>fuer</mtext></mrow><mspace width="1em"></mspace><mi>j</mi><mo>=</mo><mi>l</mi><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mtd></mtr><mtr><mtd><mo>=</mo></mtd><mtd><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo stretchy="false">(</mo><mi>l</mi><mo>+</mo><mn>1</mn><mo stretchy="false">)</mo><mspace width="1em"></mspace><mrow data-mjx-texclass="ORD"><mtext>fuer</mtext></mrow><mspace width="1em"></mspace><mi>j</mi><mo>=</mo><mi>l</mi><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow></mtd></mtr></mtable></mrow></mstyle></mrow></math>
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