Solve these two questions. They are not very long. And try to write clearly and accurately!
Q1: The wave function ψk(x) of an electron in a crystal may be expressed in a Fourier series as ψk(x)=∑C(k)exp(ikx). Use this statement to prove the Bloch theorem.
Q2: Show that the wavelength associated with an electron having an energy equal to Fermi energy is given by
λF=2*sqrt(pi/(3*n))
where n seems is concentration of electrons(confirm it!).