
\sect{Baruch's  B03.}

Consider an ideal Bose gas in d dimensions whose single particle
spectrum is given by ${\epsilon =\alpha |{\bf p}|^{s}, s>0}$.

\begin{itemize}
\item [(a)]
Find the condition on ${s, d}$ for the existence of Bose-Einstein
condensation. In particular show that for nonrelativistic particles
in two dimensions ${\left(s=d=2\right)}$ the system does not exhibit
Bose-Einstein condensation.

\item [(b)]
Show that
\[\ P= \frac{s}{d}\frac{E}{V}\,\,\,\,\,\,
\mbox{and}\,\,\,\,\,\,
C_{V}(T\rightarrow \infty) = \frac{d}{s}
Nk_{B}\]\\
\end{itemize}

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