# Homework Help: Uncertainty Principle Examples in Solid State Physics

1. May 3, 2012

### mtmiec

Hi, I'm working on a homework for my solid state physics class and I'm having trouble with this question:

1. The problem statement, all variables and given/known data
"We have seen many cases in solid state physics in which you can apply the concept of uncertainty principle to estimate some quantity. Describe two examples of a phenomenon where you can apply this concept, and show the calculation associated with that example. Choose the cases which were not covered in the lecture. Come up with your own examples."

3. The attempt at a solution
I have one potential answer, an estimation of the Fermi wavevector in the free electron model of a Fermi gas. Approximating Δx (of an electron) as (1/n)1/3, where n is the charge carrier concetration, and Δp as hbar×kf gives a result for kf with the correct n dependence:

kf=(1/2)×n1/3

kf=(3π2n)1/3

I figure the uncertainty principle would more properly be used to estimate the rms electron momentum, but I think it would be better to compare my answer to an equation we used in class, and that's easy with kf. How does this answer look?

I'm having some trouble coming up with a second example to use, because I think the standard applications of the uncertainty principle might be too elementary for this class (things like the size of the hydrogen atom or the linewidth of emission lines). Also, some good examples were already covered in class.

I feel like there should be a good example involving phonons, because momentum is so explicitly involved, but even so I can't think of a good way to apply the principle here. I'm not looking for any math or explicit answers, just some ideas.

Your help is greatly appreciated! Thanks!

Last edited: May 3, 2012