1. The problem statement, all variables and given/known data I have to find the linear combinations of Y_10, Y_11, and Y_1-1 that are eigenfunctions of L_y. There are three such combinations... 2. Relevant equations 3. The attempt at a solution Starting from (L_y)(psi_y)=(alpha)(psi_y), Using the relationshiP: psi_y= aY_11 + bY_10 + cY_1-1 And: L_y=(i/2)(L_(-) - L_(+)) I solved it to the point where I got to: (alpha)(psi_y) = (alpha)aY_11 + (alpha)bY_10 + (alpha)cY_1-1 = (i/sqrt(2))(bY_1-1 - bY_11 + (a-c)Y_10) What I have to solve is this system of equations for when alpha=0, 1, -1: (ib/sqrt(2)) = (alpha)c (-ib/sqrt(2) = (alpha)a i(a-c)/sqrt(2) = (alpha)b So for instance, when alpha=-1, the answers I know are: a=1/2, c=-1/2, b=-i/sqrt(2). Which gives one of the three linear combinations: psi_y=(1/2)Y_11 - (i/sqrt(2))Y_10 - (1/2)Y_1-1. However, I have no idea how to solve that system of equations, though I really feel like I should :( So I guess it really boils down to me not knowing the math..... help..?