1. Sketch the phase space of a weight free falling along the z coordinate (no motion in other directions). Sketch the trajectory of the free fall including impact on the ground. 2. Calculate the density of states, entropy, and temperature (all as a function of energy) for the following model: Consider a 1 dimensional lattice with 3 elds (periodic boundary conditions). Every lattice site can have the states ; 0; +. Interaction energies are only between nearest neighbors and are E() = +4 E(++) = +3 E(+) = E(+) = 2 everything else E = 0. Sketch the highest and lowest energy states. 3. Dierences: CanonicalMicrocanonical ensemble Assume you have given a density of states as a function of energy (E). This can be used to calculate canonical and microcanonical data. (a) Discretize Energy in units of E and write down the entropy microcanoni- cally. (b) Give the partition sum in the canonical and the microcanonical ensemble (as a function of the relevant observables). (c) Assume you measure an observable as a function of energy A(E). Write down its average canonically and microcanonically. 2. 3. I don't know how to sketch in problem 1 and for problem 2, I think maybe there are mistakes in the problem, otherwise, the highest energy should be +∞ and the lowest is -∞. Problem 3 I totally have no idea of it, and I want to know the difference and relation between Ω(the number of microstates) and Ω'(the density of states).