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\sect{The ergodic microcanonical density}

Find an expression for ${\rho\left(x\right)}$ of a particle which is
confined by a potential ${V\left(x\right)}$, assuming that the its
state is microcannonical with energy ${E}$. Distinguish the special
cases of ${d=1,2,3}$ dimensions. In particular show that in the in
the ${d=2}$ case the density forms a step function. Contrast your
results with the canonical expression ${\rho\left(x\right) \propto
exp\left(-\beta V\left(x\right)\right)}$.





