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Display information for equation id:math.1130.17 on revision:1130
* Page found: Effektives Potential (eq math.1130.17)
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TeX (original user input):
d\varphi =\frac{{{L}^{2}}}{\mu {{r}^{2}}}\frac{dr}{\sqrt{\frac{2}{\mu }\left( E-U \right)}}=\frac{{{L}^{2}}}{{{r}^{2}}}\frac{dr}{\sqrt{2\mu \left( E-U \right)}}=\frac{{{L}^{2}}}{{{r}^{2}}}\frac{dr}{\sqrt{2\mu E-\frac{L_{z}^{2}}{{{r}^{2}}}+\frac{2\mu \alpha }{r}}}
TeX (checked):
d\varphi ={\frac {{L}^{2}}{\mu {{r}^{2}}}}{\frac {dr}{\sqrt {{\frac {2}{\mu }}\left(E-U\right)}}}={\frac {{L}^{2}}{{r}^{2}}}{\frac {dr}{\sqrt {2\mu \left(E-U\right)}}}={\frac {{L}^{2}}{{r}^{2}}}{\frac {dr}{\sqrt {2\mu E-{\frac {L_{z}^{2}}{{r}^{2}}}+{\frac {2\mu \alpha }{r}}}}}
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MathML (2.9 KB / 377 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>d</mi><mi>φ</mi><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>L</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>μ</mi><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>r</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow><mrow data-mjx-texclass="ORD"><mi>μ</mi></mrow></mfrac></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>E</mi><mo>−</mo><mi>U</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></msqrt></mrow></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>L</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>r</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>μ</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>E</mi><mo>−</mo><mi>U</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></msqrt></mrow></mrow></mfrac></mrow><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msup><mi>L</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow><mrow data-mjx-texclass="ORD"><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>d</mi><mi>r</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msqrt><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>μ</mi><mi>E</mi><mo>−</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><msubsup><mi>L</mi><mrow data-mjx-texclass="ORD"><mi>z</mi></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msubsup></mrow><mrow data-mjx-texclass="ORD"><msup><mi>r</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo>+</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>2</mn><mi>μ</mi><mi>α</mi></mrow></mrow><mrow data-mjx-texclass="ORD"><mi>r</mi></mrow></mfrac></mrow></mrow></msqrt></mrow></mrow></mfrac></mrow></mstyle></mrow></math>
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