I do not understand this question.

We aim to evaluate the optical absorption by electrons in a quantum well. The distinction from problem 1 is that the electron are confined in a quantum well in the z direction, but are free particles in the x and y directions. We consider the following wave functions for the initial and final states: 1 Hi(T)= eiki, un (z) VA 1 Uf (r ) = VA pik rui(z)Here la. and E'are wavewvectors in x-y plane, and represent the initial and nal momenta up to a factor 3%, 1,0,, (2) and wine) are the wave-function of the n~th and Lth level in a square well in the : direction, and A is the area of the sample in the x-y plane. The transition between the initial and nal states due to optical (photon) absorption is determined by the following matrix element: g); 2 M); (met-EM\"2 tbdf', where Eph is the electromagnetic wave (photon) wave~vector, and 35' is the momentum operator. The wave-length of the EM wave is typically much larger than the well width, and EM can point in any direction in the 3D space. (a) (30 points) Evaluate the x, y, and 3 components ofif. What relation E, if", and Km should satisfy for optical (photon) absorption to take place? (b) (10 points) What direction of the electric eld of the EM wave (polarization) will result in optical absorption? (c) (10 points) What condition the vels n and I should satisfy in order for a transition between 1!},- and 1,1), to occur