Consider a mechanical system with energy AND=(p2 /2m)+ax2bx2where and are constants. Suppose the system is isolated and the energy conserved in the microcannonical ensemble? Plot out the constant energy curves in phase space for different positive values of and . What do the contours look like? Consider this mechanical system again in the canonical ensemble with some temperature . Do not calculate, but consider the canonical Boltzmann distribution function (, ). Is the momentum distribution correlated with the positional distribution? Sketch out the positional part of the Boltzmann distribution function () (this can be done in your graphing calculator or matlab). The overall constant (partition function) does not change the shape of the curve, but only scale the overall plot, so can be neglected. Indicate how constants such as and influence the plot. As you vary and , how does the plot change? What is the expected average value of , i.e., ?