midterm_02 - Solutions to midterm 2 (141A Sp 07) 1 1. (a)...

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Unformatted text preview: Solutions to midterm 2 (141A Sp 07) 1 1. (a) Blochs theorem says that if the potential is periodic, ie. U ( ~ x + ~ a ) = U ( ~ x ), then the energy eigenfunctions satisfy ( ~ x + ~ a ) = e i ~ k ~ a ( ~ x ) for some ~ k . This is important for a number of reasons. For instance, it shows that the eigenfunctions are extended in space and can be labeled with a momentum-like quantum number, thus justifying the free electron model for metals. (b) The Wiedemann-Franz law says that, for metals, the ratio / ( T ) is independent of the material and amount of disorder. Since this result is derived from the free-electron model, it provides an experimental justification of that model. (c) For BiTe 2 , we have the bismuth contributing 2 + 3 = 5 electrons, and each tellurium 2 + 4 = 6 electrons. This gives a total of 17 electrons per unit cell. Since each band can take 2 electrons per unit cell, this means that we will have 8 filled bands and one half filled band, suggesting that this material is a metal....
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This note was uploaded on 08/01/2008 for the course PHYSICS 141A taught by Professor Souza during the Spring '08 term at University of California, Berkeley.

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midterm_02 - Solutions to midterm 2 (141A Sp 07) 1 1. (a)...

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