Consider a system of n interacting molecules, whose vibrational degrees of freedom are treated with qm, and whose translational and rotational degrees of freedom are treated classically with the hamiltonian: hclass = ktrans + krot + u where k is kinetic energy, and u is a potential energy. derive the expression: prob(ktrans) = e −ktrans kt dptrans ∫ e −ktrans kt dptrans by starting from: q = qqm n! h sn ∫ e hclass kt dpclass dqclass given that: ktrans = ∑ 1 2m n j=1 (px, j 2 + py, j 2 + pz, j 2 ) derive the normalized maxwell-boltzmann distribution: f(px , py, pz)dpxdpydpz = (2πmkt) −3/2 e −(px 2+py 2+pz 2) 2mkt dpxdpydpz