Physics 115A   Spring 2001

		Statistical Physics 		due 12:30 pm Thursday, April 12

PROBLEM SET 1

Reading: Chapter 1 (especially sections 1.1-1.6 and last paragraph of page 39) and Chapter 2 in Reif.

Hint: Notice that there are many helpful mathematical appendices in Reif.

1.

Show explicitly that the following identities are correct for the Gaussian function

$$P(x)dx=\frac{1}{\sqrt{2\pi}\sigma}e^{-(x-\mu)^2/2\sigma^2}dx$$

(a)

Normalization

$$\int^{\infty}_{-\infty} dx P(x)=1$$

(b)

Mean or average value

$$\mu=\int^{\infty}_{-\infty} dx P(x)x$$

(c)

Variance or second moment of the distribution

$$\sigma^2=\overline{(x-\mu)^2}$$

2.

Reif 1.9

3.

Reif 1.10

4.

Reif 1.11

5.

Reif 2.1