a) For the given parameters, explicitly construct and Ψa(x) and Ψb(x) for the Kronig- Penney model. Plot Ψ*Ψ over 2 periods of the potential.

(a+b) = 5 Å (corresponds to atomic spacing) a=1Å

b=4Å

U0 = 2.4 eV

Second lowest energy band k = π/(2(a+b))

b)Show that the wavefunction is the same if k = 5π/(2(a+b)) (this would be in the second Brillouin zone)

c) What is the energy of this state? Is E>U0 or is E<U0?

(a+b) = 5 Å (corresponds to atomic spacing) a=1Å

b=4Å

U0 = 2.4 eV

Second lowest energy band k = π/(2(a+b))

b)Show that the wavefunction is the same if k = 5π/(2(a+b)) (this would be in the second Brillouin zone)

c) What is the energy of this state? Is E>U0 or is E<U0?