Update 11_nearly_free_electron_model_solutions.md - update

src/11_nearly_free_electron_model_solutions.md

@@ -163,13 +163,13 @@ and
 =& -\kappa \lambda \sum_{m \neq 0 } e^{-\kappa a|m-1|} e^{-\kappa a |m|} =-\kappa \lambda(e^{ka}+e^{-ka}) \sum_{m=1}^{m=\infty} e^{-2\kappa a m}
 \end{align}
 
-In the limit $\kappa a \gg 1$ (i.e., where the distance between the delta functions is large compared to the width of $|n\rangle$), the onsite energy becomes
+In the limit $\kappa a \gg 1$ (i.e., where the distance between the delta functions is large compared to the width of the isolated orbitals), the onsite energy becomes
 $$
-\langle n|H|n \rangle = \epsilon_0(1-4 e^{-2\kappa a})
+\langle n|H|n \rangle = \epsilon_0(1-4 e^{-2\kappa a}) 
 $$
 and the hopping becomes
 $$
-\langle n-1|H|n \rangle = \epsilon_0 (\kappa a  - 2) e^{-\kappa a}
+\langle n-1|H|n \rangle = \epsilon_0 (\kappa a  - 2) e^{-\kappa a} \approx \epsilon_0 \kappa a e^{-\kappa a}
 $$
 
 ### Subquestion 4