Here is a problem that you can do if you like. It is optional, but if you want to email me your answer to the last part (what is it as a fraction of the speed of light, c?) you'll get extra credit. It provides a chance to calculate actual numbers again and it is related to something we will cover tomorrow in class.
5. Consider the expression \(E_{1,k} = E_1 -2 \gamma_1 cos(ak)\). Suppose gamma = 2 eV.
Calculate the group velocity \(v(k) = \frac{1}{\hbar}\frac{\partial E_{1,k} }{\partial k }\). Graph it vs k and evaluate it at its maximum value. I think it is at \(k = \pi/2a\). What is it as a fraction of the speed of light, c?
hint:
multiply top and bottom by c and use \(\hbar c =197\) eV-nm like before (see HW 1a post)
Someone pointed out in an email that we need a given value of a to actually do this. Good insight! Thanks.
ReplyDeleteLet's use a=0.2 nm