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Course: PHYS 7, Spring 2012
School: Berkeley
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of 1 University California, Berkeley Physics H7C Fall 1999 (Strovink) PROBLEM SET 12 1. Rohlf 12.5. 6. Rohlf 18.11. 2. N electrons each of mass m are conned within a (formerly) cubic innite potential well that has been squashed almost at: V = 0 for (0 &lt; x &lt; L and 0 &lt; y &lt; L and 0 &lt; z &lt; L), V = otherwise. Here 1 (cube is squashed in the z direction) and N 1. The electrons...

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of 1 University California, Berkeley Physics H7C Fall 1999 (Strovink) PROBLEM SET 12 1. Rohlf 12.5. 6. Rohlf 18.11. 2. N electrons each of mass m are conned within a (formerly) cubic innite potential well that has been squashed almost at: V = 0 for (0 < x < L and 0 < y < L and 0 < z < L), V = otherwise. Here 1 (cube is squashed in the z direction) and N 1. The electrons do not interact with each other and are at very low temperature so that they ll up the available states in order of increasing energy. Take N 1, so that the z part of each electrons wavefunction may be assumed to be the same (lowest possible kz ). Thus the problem is reduced to two dimensions. Calculate the dierence energy between the of the most energetic electron (Fermi energy) and the energy of a ground state electron, using the approximation N 1. should depend on m, N , and L, but not . 7. Rohlf 19.18. 3. Write an integral equation for the fraction F of nonrelativistic fermions in a gas at nite temperature T which have energy above the Fermi energy EF . The density of states is proportional to E 1/2 and the probability that a state is occupied is 1 exp (E EF ) + 1 where = (kT )1 . You dont need to perform the integration, but you should set up the integral so that doing it would yield the correct answer without any additional physical reasoning. 4. Rohlf 12.16. 5. Rohlf 17.27. 8. Rohlf 19.29.
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data = [8.5831860.5351168.7874157.8122682.16152516.17389615.9179978.9451389.3762889.2226036.5736845.40022913.33013210.4008767.03721612.97136714.0984729.59484415.8425599.7144588.4411964.8677898.6051567.0818550.16325710.13243614.39
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