Energie: Difference between revisions
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<source lang="text"> | <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; | ||
Energy := Sqrt[Subscript[m, 0]^2*c^4 + p^2*c^2]; | |||
EnergyAppox := Series[Energy, {p, 0, 5}] // Simplify; | |||
Print["E" == | |||
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> | ||
[[Kategorie:Definition]] | [[Kategorie:Definition]] | ||
Revision as of 19:44, 11 July 2009
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]