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Display information for equation id:math.2720.23 on revision:2720
* Page found: Fermis Goldene Regel (eq math.2720.23)
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Hash: 153a88c94bed67abc57a9efbed17e46f
TeX (original user input):
{{\left| \int\limits_{0}^{t}{dt'\,\,{{e}^{\text{i}\left( {{E }_{f}}-{{E }_{i}} \right)t'}}} \right|}^{2}}={{\left| \frac{{{e}^{\text{i}\left( {{E }_{f}}-{{E }_{i}} \right)t}}-1}{\text{i}\left( {{E }_{f}}-{{E }_{i}} \right)} \right|}^{2}}=\frac{{{\sin }^{2}}\left( \frac{{{E }_{f}}-{{E }_{i}}}{2}t \right)}{{{\left( \frac{{{E }_{f}}-{{E }_{i}}}{2} \right)}^{2}}}={{t}^{2}}{{\operatorname{sinc}}^{2}}\left( \frac{{{E }_{f}}-{{E }_{i}}}{2}t \right)
TeX (checked):
{{\left|\int \limits _{0}^{t}{dt'\,\,{{e}^{{\text{i}}\left({{E}_{f}}-{{E}_{i}}\right)t'}}}\right|}^{2}}={{\left|{\frac {{{e}^{{\text{i}}\left({{E}_{f}}-{{E}_{i}}\right)t}}-1}{{\text{i}}\left({{E}_{f}}-{{E}_{i}}\right)}}\right|}^{2}}={\frac {{{\sin }^{2}}\left({\frac {{{E}_{f}}-{{E}_{i}}}{2}}t\right)}{{\left({\frac {{{E}_{f}}-{{E}_{i}}}{2}}\right)}^{2}}}={{t}^{2}}{{\operatorname {sinc} }^{2}}\left({\frac {{{E}_{f}}-{{E}_{i}}}{2}}t\right)
LaTeXML (experimentell; verwendet MathML) rendering
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MathML (4.015 KB / 498 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><munderover><mo form="prefix" texclass="OP">∫</mo><mrow data-mjx-texclass="ORD"><mn>0</mn></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></munderover><mrow data-mjx-texclass="ORD"><mi>d</mi><msup><mi>t</mi><mo>′</mo></msup><mspace width="0.167em"></mspace><mspace width="0.167em"></mspace><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>i</mtext></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub><mo>−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><msup><mi>t</mi><mo>′</mo></msup></mrow></mrow></msup></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mstyle><mo>=</mo><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"><msup><mi>e</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>i</mtext></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub><mo>−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow><mi>t</mi></mrow></mrow></msup><mo>−</mo><mn>1</mn></mrow></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mtext>i</mtext></mrow><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub><mo>−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo>=</mo><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msup><mi>sin</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></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>E</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub><mo>−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></mrow><mrow data-mjx-texclass="ORD"><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>E</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub><mo>−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mo data-mjx-texclass="CLOSE">)</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></mrow></mfrac></mrow><mo>=</mo><msup><mi>t</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><msup><mi data-mjx-texclass="OP" mathvariant="normal">sinc</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></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>E</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub><mo>−</mo><msub><mi>E</mi><mrow data-mjx-texclass="ORD"><mi>i</mi></mrow></msub></mrow></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></mfrac></mrow><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow></mrow></math>
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