Nur zu Testzwecken: E = c 2 p 2 + m 2 c 4 = c 2 ⋅ ( p 2 + m 2 c 2 ) = c ⋅ p 2 + m 2 c 2 {\displaystyle E={\sqrt {c^{2}p^{2}+m^{2}c^{4}}}={\sqrt {c^{2}\cdot (p^{2}+m^{2}c^{2})}}=c\cdot {\sqrt {p^{2}+m^{2}c^{2}}}}
E ′ ( p ) = c p p 2 + m 2 c 2 {\displaystyle E'(p)={\frac {cp}{\sqrt {p^{2}+m^{2}c^{2}}}}}
E ″ ( p ) = c p 2 + m 2 c 2 − c 2 p 2 p 2 + m 2 c 2 p 2 + m 2 c 2 {\displaystyle E''(p)={\frac {c{\sqrt {p^{2}+m^{2}c^{2}}}-{\frac {c^{2}p^{2}}{\sqrt {p^{2}+m^{2}c^{2}}}}}{p^{2}+m^{2}c^{2}}}}
T ( p ) = 1 0 ! ⋅ m c 2 + 1 1 ! ⋅ 0 p + 1 2 ! ⋅ m c 2 m 2 c 2 ⋅ p 2 = m c 2 + p 2 2 m = m c 2 + 1 2 m v 2 {\displaystyle T(p)={\frac {1}{0!}}\cdot mc^{2}+{\frac {1}{1!}}\cdot 0p+{\frac {1}{2!}}\cdot {\frac {mc^{2}}{m^{2}c^{2}}}\cdot p^{2}=mc^{2}+{\frac {p^{2}}{2m}}=mc^{2}+{\frac {1}{2}}mv^{2}}
