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\begin{document}

\csection{Ph 340 -- Problem Set 1 -- Spring 1997}

\begin{enumerate}
\item
A particular particle has (in one space dimension) a four-momentum
$\underline{p} = ( p , E /c ) = ( 80 \unit{GeV/c} , 100 \unit{GeV/c}
)$.
\begin{enumerate}
\item
Compute the mass of the particle.
\item
Compute the speed of the particle.
\item
Compute the frequency and wavenumber of the associated matter wave.
\item
Compute the phase speed of the associated matter wave.
\item
Compute the group velocity of a relativistic wave packet with the
central wavenumber obtained above.
\end{enumerate}
\item
Modify the demonstration file {\tt packet\_demo.r} to demonstrate the
behavior of the wave packet associated with a relativistic particle
with the central wavenumber equal to the wavenumber obtained in part (c)
of the above problem.  Obtain a plot of the development of such a
wave packet.
\end{enumerate}

\end{document}
