
\sect{Baruch's  B06.}

Consider an ideal Bose gas  with spin 1 in a magnetic field $B$.
The Hamiltonian for each particle is ${\cal
H}=\frac{{\bf p}^2}{2m}-\gamma BS_z$ where $S_z=1,0,-1$ and $\gamma$ is
the gyromagnetic ratio. The average density is $n$ and particle
mass is $m$.
\begin{itemize}
\item[(a)]  Particles of which $S_z$ can
condense? Find an equation for the condensation temperature $T_c$.
Solve this equation explicitly for (i) $B=0$, and (ii) large $B$,
$\gamma B\gg k_BT_c$; keep the lowest order correction.
\item[(b)] Plot, qualitatively, $T_c(B)/T_c(\infty)$  as function of $B$.
If $T$ is below but close to the value of
$T_c(B\rightarrow \infty)$  describe what happens as $B$ is
increased from $B=0$. Find the critical $B$ for condensation in
the limit of (a-ii).
\item[(c)] Evaluate the specific heat in the limit of (a-ii).
\item[(d)] Evaluate the condensate  fraction $\langle n_0\rangle/n$ as function of $T$ in the case of (a-ii).
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\end{itemize}

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