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* Page found: Fermis Goldene Regel (eq math.2720.23)

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{{\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)

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MathML (29.752 KB / 3.537 KB) :

| ∫ 0 t 𝑑 t ′ ⁢ e i ⁢ ( E f - E i ) ⁢ t ′ | 2 = | e i ⁢ ( E f - E i ) ⁢ t - 1 i ⁢ ( E f - E i ) | 2 = sin 2 ⁡ ( E f - E i 2 ⁢ t ) ( E f - E i 2 ) 2 = t 2 ⁢ sinc 2 ⁡ ( E f - E i 2 ⁢ t ) superscript superscript subscript 0 𝑡 differential-d superscript 𝑡 ′ superscript 𝑒 i subscript 𝐸 𝑓 subscript 𝐸 𝑖 superscript 𝑡 ′ 2 superscript superscript 𝑒 i subscript 𝐸 𝑓 subscript 𝐸 𝑖 𝑡 1 i subscript 𝐸 𝑓 subscript 𝐸 𝑖 2 superscript 2 subscript 𝐸 𝑓 subscript 𝐸 𝑖 2 𝑡 superscript subscript 𝐸 𝑓 subscript 𝐸 𝑖 2 2 superscript 𝑡 2 superscript sinc 2 subscript 𝐸 𝑓 subscript 𝐸 𝑖 2 𝑡 {\displaystyle{\displaystyle{{\left|\int\limits_{0}^{t}{dt^{\prime}\,\,{{e}^{% \text{i}\left({{E}_{f}}-{{E}_{i}}\right)t^{\prime}}}}\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)}}

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|∫0tdt′ei(Ef−Ei)t′|2=|ei(Ef−Ei)t−1i(Ef−Ei)|2=sin2(Ef−Ei2t)(Ef−Ei2)2=t2sinc2(Ef−Ei2t)

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Abgerufen von „https://wiki.physikerwelt.de/wiki/Spezial:Formelinformation“