HW 2 Solutions

Please comment here regarding if any aspects of these solutions are not clear or may be incorrect or different from what you got. I thought the \(k = \pi/2a\) and the  \(k = -\pi/2a\)  states turned out to be pretty interesting. There is a real part and an imaginary part. The two states differ in terms of the sign of the imaginary part of the wave-function; the real parts are exactly the same. Although they have the same energy, they are very different states. One propagates to the right; the other propagates to the left. Note also that every state in the band has the same \(|\psi|^2\) and yet they each different and have different energies, etc.

For the question about dividing the energies the band into three equal parts (2.1c), was the answer 9, 2, 9 or maybe 8, 4, 8? or something else? What did you get?