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Display information for equation id:math.2719.25 on revision:2719
* Page found: Fermis Goldene Regel (eq math.2719.25)
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Hash: b32d3675445a733e8923e120241a67cc
TeX (original user input):
{{\Gamma }_{i\to f}}={{\left| \left\langle f \right|V\left| i \right\rangle \right|}^{2}}\pi \underset{t\to \infty }{\mathop{\lim }}\,\frac{t}{\pi }{{\operatorname{sinc}}^{2}}\left( \frac{{{E }_{f}}-{{E }_{i}}}{2}t \right)=2\pi {{\left| \left\langle f \right|V\left| i \right\rangle \right|}^{2}}\delta \left( {{E }_{f}}-{{E }_{i}} \right)
TeX (checked):
{{\Gamma }_{i\to f}}={{\left|\left\langle f\right|V\left|i\right\rangle \right|}^{2}}\pi {\underset {t\to \infty }{\mathop {\lim } }}\,{\frac {t}{\pi }}{{\operatorname {sinc} }^{2}}\left({\frac {{{E}_{f}}-{{E}_{i}}}{2}}t\right)=2\pi {{\left|\left\langle f\right|V\left|i\right\rangle \right|}^{2}}\delta \left({{E}_{f}}-{{E}_{i}}\right)
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MathML (2.477 KB / 467 B) :
<math class="mwe-math-element" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi mathvariant="normal">Γ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo accent="false">→</mo><mi>f</mi></mrow></mrow></msub></mstyle><mo>=</mo><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>f</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mi>V</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>i</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>π</mi><mrow data-mjx-texclass="ORD"><munder><mrow data-mjx-texclass="OP"><mi>lim</mi></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi><mo accent="false">→</mo><mi mathvariant="normal">∞</mi></mrow></munder></mrow><mspace width="0.167em"></mspace><mrow data-mjx-texclass="ORD"><mfrac><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow><mrow data-mjx-texclass="ORD"><mi>π</mi></mrow></mfrac></mrow><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><mo>=</mo><mn>2</mn><mi>π</mi><msup><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">⟨</mo><mi>f</mi><mo data-mjx-texclass="CLOSE">|</mo></mrow><mi>V</mi><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">|</mo><mi>i</mi><mo data-mjx-texclass="CLOSE">⟩</mo></mrow><mo data-mjx-texclass="CLOSE">|</mo></mrow><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mi>δ</mi><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></math>
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