Given the quantum mechanical energy levels of a particle in a two-dimensional box are h2 y 1,2,3 8ma2(s^+s) calculate the density of states ω(e)de and use this to find the translational partition function of the two-dimensional ideal gas. derive the function using an alternative method [hint: q'eeny may be expressed using an integral] (i) (ii) iii find the equation of state, the energy e, the heat capacity ca and the entropy. (note: a → area, compare with v → volume in 3d case)