Review Note
Last Update: 12/29/2024 03:09 PM
Current Deck: Physik::T2
Published
Fields:
Front
Für welches \(\omega \) ist \(\phi (\vec x, t) =e^{i(\vec k \vec x - \omega t)}\) eine Lösung von \(\Box \phi = 0\) ?
Back
\(\omega = c\cdot |\vec k|\) ...Dispersionsrelation
Rechnung:
\(\phi (\vec x, t) =e^{i(\vec k \vec x - \omega t)}\)
\(\Box := \Delta - \frac{1}{c^2} \frac{\partial^2}{\partial t^2}\)
\(\Rightarrow\Box \phi =(-\frac{1}{c^2}(-i\omega)^2+(ik)^2)\phi \)
\(= (\frac{\omega^2}{c^2}-\vec k^2)\phi \ \ \ \ ... \ \ \omega = c\cdot |\vec k|\)
\(= 0\)
Rechnung:
\(\phi (\vec x, t) =e^{i(\vec k \vec x - \omega t)}\)
\(\Box := \Delta - \frac{1}{c^2} \frac{\partial^2}{\partial t^2}\)
\(\Rightarrow\Box \phi =(-\frac{1}{c^2}(-i\omega)^2+(ik)^2)\phi \)
\(= (\frac{\omega^2}{c^2}-\vec k^2)\phi \ \ \ \ ... \ \ \omega = c\cdot |\vec k|\)
\(= 0\)
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