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\sect{The functions $N(E)$ and $Z(T)$ for a particle in a double well}
Consider a particle that has a mass $m$ in a double well.
The potenial $V(x)$ of the well is described in the figure.
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\begin{itemize}
\item[(a)]
Describe the possible trajectories of the particle in the double well.
\item[(b)]
Calculate ${N(E)}$ and the energy levels in the semi-classical approximation.
\item[(c)]
Calculate ${Z(\beta)}$ and show that it can be written
as a product of "kinetic" term and "spin" term.
\end{itemize}