Physics 115A       Fall 2013

Statistical Physics due 9:30 am Tuesday, Oct 8

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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.

  1. Show explicitly (by hand, not mathematica) that the following identities are correct for the Gaussian function
    ---1-- - (x-μ)2∕2σ2 P (x)dx = √2-π-σe dx

    1. Normalization
      ∫ ∞ dxP (x ) = 1 -∞

    2. Mean or average value
      ∫ ∞ μ = dxP (x)x -∞

    3. Variance or second moment of the distribution
      --------- σ2 = (x - μ )2

  2. Reif 1.9
  3. Reif 1.10
  4. Reif 1.11
  5. Reif 1.19
  6. Reif 2.1