% Bernd Berg sep 21 2017.
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\centerline{\bf Special and General Relativity (PHZ 4601/5606) Fall 2017 
Solutions} \medskip

\centerline{\bf Set 5} 

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% \end{figure} \centerline{Potential as function of $z$.}

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\item{\bf 17. An astrophysical observation (redshift). } \smallskip
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\noindent The equation for the redshift is
\begin{eqnarray} \nonumber
  \lambda'\ =\ \lambda\,\sqrt{\frac{1+\beta}{1-\beta}}\ &\Rightarrow&\
  \left(\frac{\lambda'}{\lambda}\right)^2\ =\ {\frac{1+\beta}{1-\beta}}
  \\ \nonumber
  \left(\frac{\lambda'}{\lambda}\right)^2 -\beta\,
  \left(\frac{\lambda'}{\lambda}\right)^2 &=& 1+\beta
  \\ \nonumber
  \left(\frac{\lambda'}{\lambda}\right)^2 - 1\ =\ \beta\,\left[ 1
  + \left(\frac{\lambda'}{\lambda}\right)^2 \right]\ &\Rightarrow&\
  \beta\ =\ \frac{(\lambda'/\lambda)^2-1}{(\lambda'/\lambda)^2+1}\,.
\end{eqnarray}
With $\lambda'=(729.2\,[nm])\,m^2/(m^2-4)$ given and from Quantum 
Mechanics books $\lambda=(364.56\,[nm]) \,m^2/(m^2-4)$ we find
$$ \beta\ =\ \frac{v}{c}\ =\ 0.6\,.$$
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