## PHYS 317 Reading Assignment #6

Read section 2.4 and answer the following questions by email, hardcopy, or web form before class Friday, September 12.

1. Is NN an overestimate or underestimate for N! ? In the more accurate estimate (aN)N, what is a?

NN is an overestimate, and (N/e)N is the more accurate estimate, so a=1/e

2. What is the ratio of (q+N)! to (q+N-1)! ?

This one gave you some trouble - some of you said the ratio is 1, but the ratio of the two is q+N. Think of the definition of factorial, then (q+N)! = (q+N)*(q+N-1)!.

3. Why can we write (q+N-1)! = (q+N)! when q and N are large?

Because they are very large numbers, and they differ only by a factor of q+N, which is a large number.

4. In equation (2.28), if q is huge and N is huge, then the width x gets pretty big also. Why does this correspond to a narrow peak? (i.e., in what sense is this narrow?)

x = q/2*sqrt(N). While this gets big when q gets big, it's still smaller than q itself by a factor of sqrt(N). So plotting on the scale of q, x is pretty small.

5. Was there anything you had particular difficulty with in this reading? Is so, describe briefly.