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> | ||
[[Taylor-Entwicklung]] für kleine Geschwindigkeiten: | [[Taylor-Entwicklung]] für kleine Geschwindigkeiten: | ||
<source> | <source lang="text"> | ||
$Assumptions = c > 0 && Subscript[m, 0] >= 0 && p >= 0 && v >= 0; | $Assumptions = c > 0 && Subscript[m, 0] >= 0 && p >= 0 && v >= 0; | ||
\[CapitalEpsilon] := | \[CapitalEpsilon] := | ||
| Line 8: | Line 8: | ||
Print["E" == \[CapitalEpsilon]]</source> | Print["E" == \[CapitalEpsilon]]</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> | ||
[[Kategorie:Definition]] | |||
Revision as of 19:40, 11 July 2009
Taylor-Entwicklung für kleine Geschwindigkeiten:
$Assumptions = c > 0 && Subscript[m, 0] >= 0 && p >= 0 && v >= 0;
\[CapitalEpsilon] :=
Series[Sqrt[Subscript[m, 0]^2*c^4 + p^2*c^2], {p, 0, 5}] //
Simplify;
Print["E" == \[CapitalEpsilon]]