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Display information for equation id:math.2717.24 on revision:2717
* Page found: Fermis Goldene Regel (eq math.2717.24)
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Hash: a353af3cf05c6234ab87d30cd2e9acfa
TeX (original user input):
{{\Gamma }_{i\to f}}:=\underset{t\to \infty }{\mathop{\lim }}\,\frac{1}{t}{{P}_{i\to f}}\left( t \right)={{\left| \left\langle f \right|V\left| i \right\rangle \right|}^{2}}\underset{t\to \infty }{\mathop{\lim }}\,t{{\operatorname{sinc}}^{2}}\left( \frac{{{\varepsilon }_{f}}-{{\varepsilon }_{i}}}{2}t \right)
TeX (checked):
{{\Gamma }_{i\to f}}:={\underset {t\to \infty }{\mathop {\lim } }}\,{\frac {1}{t}}{{P}_{i\to f}}\left(t\right)={{\left|\left\langle f\right|V\left|i\right\rangle \right|}^{2}}{\underset {t\to \infty }{\mathop {\lim } }}\,t{{\operatorname {sinc} }^{2}}\left({\frac {{{\varepsilon }_{f}}-{{\varepsilon }_{i}}}{2}}t\right)
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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"><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><mi>:</mi><mo>=</mo><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"><mn>1</mn></mrow><mrow data-mjx-texclass="ORD"><mi>t</mi></mrow></mfrac></mrow><msub><mi>P</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>i</mi><mo accent="false">→</mo><mi>f</mi></mrow></mrow></msub><mrow data-mjx-texclass="INNER"><mo data-mjx-texclass="OPEN">(</mo><mi>t</mi><mo data-mjx-texclass="CLOSE">)</mo></mrow><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><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><mi>t</mi><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>ε</mi><mrow data-mjx-texclass="ORD"><mi>f</mi></mrow></msub><mo>−</mo><msub><mi>ε</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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