Hints for problem #1: 1,2,3, are straightforward. For 4, you have to figure out how to change the ket into a bra so that you can do < V | Y > For 5, and 6 look at page 7 of the lecture notes. You have to find the value |Y_{E_1}> and |Y_{E_2}> and then renormalize them. Also, for 4,5, and 6 you can set: |Y> = y_1 * |1> + y_2 * |2> + y_3 * |3> (and similarly for the others) and then just show the algebra for calculating < V | Y > for part 4 and | Z > for parts 5, and 6. David