Physics 115A xxxxx Fall 2013 Statistical Physics due 9:30 am Tuesday, Oct 8

PROBLEM SET 1

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

Problems:

Hint: Notice that for analytical calculations, there are many helpful mathematical appendices in Reif.

Show explicitly (by hand, not mathematica) that the following identities are correct for the Gaussian function

. P (x)dx = \frac{1}{\sqrt{2π}σ} e^{−(x−μ)^{2}/2σ^{2}}dx

Normalization . ∫_{−∞}^{∞} dxP (x) = 1 Mean or average value . μ = ∫_{−∞}^{∞} dxP (x)x Variance or second moment of the distribution . σ^{2} = \overline{(x − μ)^{2}}

Reif 1.9 Reif 1.10 Reif 1.11 Reif 1.19 Reif 2.1