Energie: Difference between revisions
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<math>E^2=m^2 c^4 + \underline{p}^2 c^2</math> | <math>E^2=m^2 c^4 + \underline{p}^2 c^2</math> | ||
mit Impuls | |||
folgt | :<math>\left| \underline{p} \right|=\gamma {{m}_{0}}\left| \underline{v} \right|</math> folgt <math>E=\gamma {{m}_{0}}{{c}^{2}}</math> | ||
<math>E=\gamma {{m}_{0}}{{c}^{2}}</math> | |||
[[Taylor-Entwicklung]] für kleine Geschwindigkeiten: | [[Taylor-Entwicklung]] für kleine Geschwindigkeiten: | ||
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Print["E" == EnergyAppox] | Print["E" == EnergyAppox] | ||
</source> | </source> | ||
<math>E=c^2 m_0+\frac{p^2}{2 m_0}-\frac{p^4}{8 \left(c^2 m_0^3\right)}+O\left(p^6\right)</math> | :<math>E=c^2 m_0+\frac{p^2}{2 m_0}-\frac{p^4}{8 \left(c^2 m_0^3\right)}+O\left(p^6\right)</math> | ||
De Brogli: | De Brogli: | ||
<math>E=\hbar \omega </math> | :<math>E=\hbar \omega </math> | ||
[[Kategorie:Mechanik]] | |||
[[Kategorie:Definition]] | [[Kategorie:Definition]] | ||
Latest revision as of 16:26, 12 September 2010
mit Impuls
Taylor-Entwicklung für kleine Geschwindigkeiten:
$Assumptions = c > 0 && Subscript[m, 0] >= 0 && p >= 0 && v >= 0;
Energy := Sqrt[Subscript[m, 0]^2*c^4 + p^2*c^2];
EnergyAppox := Series[Energy, {p, 0, 5}] // Simplify;
Print["E" == EnergyAppox]
De Brogli: