PHYS 317 Reading Assignment #7

Read section 2.5 and answer the following questions by email, hardcopy, or web form before class Monday, September 15.

1. For a 2 particle system, what is the dimension of the momentum space hypersphere?

   6. Since each particle has 3 momentum components, 2 particles have 6 momentum components, and a fixed value of p₁²/2m + p₂²/2m = U constrains these 6 components to the surface of a 6-dimensional hypersphere.

2. What is the surface area of a 4-dimensional hypersphere?

   For radius r: ``area'' = 2 (pi)² r³

3. For a system of N particles where all of its energy is contained in quadratic degrees of freedom (f per particle), the multiplicity is proportional to U raised to what power?

   Multiplicity is proportional to U^{f N/2}. This checks for the monatomic ideal gas, where f=3 and the multiplicity goes as U^3N/2.

4. What is the probability of finding all N particles of a gas on the left half of a container?

   The multiplicity with all the particles on the left half is reduced by a factor of 1/2^N, so the probability is reduced by the same factor.

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

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