## 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.

**Is N**^{N} an overestimate or underestimate for N! ? In the more accurate estimate (aN)^{N}, what is a?
N^{N} is an overestimate, and (N/e)^{N} is the more
accurate estimate, so a=1/e

**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)!.

**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.

**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.

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

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