This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Solutions to midterm 2 (141A Sp 07) 1 1. (a) Bloch’s theorem says that if the potential is periodic, ie. U ( ~ x + ~ a ) = U ( ~ x ), then the energy eigenfunctions satisfy ψ ( ~ x + ~ a ) = e i ~ k · ~ a ψ ( ~ 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 momentumlike quantum number, thus justifying the free electron model for metals. (b) The WiedemannFranz law says that, for metals, the ratio κ/ ( σ T ) is independent of the material and amount of disorder. Since this result is derived from the freeelectron 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....
View
Full Document
 Spring '08
 SOUZA
 Electron, Energy, Solid State Physics, Electrons, Van der Waals

Click to edit the document details