@@ -175,7 +175,7 @@ Let's consider a 1D crystal with a period $a$. Let $k_0$ be any wave number of a
To answer this question, only consider consider two free electron wavefunctions in the Hamiltonian and ignore all the others. Between what two of free electron wavefunctions does the coupling give significant contribution to the energy levels of the free electron wavefunctions?
#### Exercise 3: the tight binding model vs. the nearly free electron model
Consider a 1D crystal with a periodic potential given by delta peaks: $$V(x) = -\lambda \sum_{n=-\infty}^{\infty} \delta(x+na),$$ where $\lambda>0$. In this exercise, we will find find the band structure of this crystal in two ways:
Consider a 1D crystal with a periodic potential given by delta peaks: $$V(x) = -\lambda \sum_{n=-\infty}^{\infty} \delta(x+na),$$ where $\lambda>0$. In this exercise, we will find the band structure of this crystal in two ways:
- By means of the nearly free electron model explained in this lecture.
- By means of the tight binding model explained in [lecture 7](/7_tight_binding).
