I do not understand how the answer to question 2.2 is constructed, is this done by applying the method for the free electron that is used in the lecture notes and inserting \delta k = k_0 + \frac{2\pi n}{a} in the formula for E?
The energy we are looking for is
E_n = \frac{\hbar^2}{2m}(k_0+\frac{2\pi n}{a})^2
To add, what is the \Omega in the formula for the wave function?
Thanks!