2. (a) Prove that the multiplicity can be approximated as ? (N, q) Kevin(q'Me when q>>N, where N is the number of oscillators in a solid and q is the number of phonons in the solid. You may start using the equations in Lecture 18, slide 24. (b) Use the result in part (a), find the width of the Gaussian peak in Lecture 18, slide 18 and 19 as a function of / and q', where / is the number of oscillators in one solid and q' is the number of total phonons in both solids