a. Consider two kets | > and | >. Suppose < | >, < |

a. Consider two kets | α > and | β >. Suppose < α’| α>, < α”| α), and < α’| β>, < α”|β), are all known, where | α’>, | α”), form a complete set of base kets. Find the matrix representation of the operator | α > < β | in that basis.

b. We now consider a spin ½ system and let | α > and | β > be | sz = h/2 | and s = h/2), respectively. Write down explicitly the square matrix that corresponds to Ia)(/I in the usual (s. diagonal) basis.