1. Operate A = yay on the function f (x, y) = e-a(x2+y2). Operate B = x _ on the same function. 2. Operate A = anz + a2 a2 a2 + - dy z - azz on f (x, y, z) = x2 + y2 + z2. Is this an eigenvalues problem? If so, what is the eigenvalue. 3. Compute the following commutators: a . f ( x ) , - in b. xn , - in c. [Px, px] where px - in ax d. [px, Py] where px - in - and where py - ihav e. [x, pyl py - in _ and x = x 4. If f(x) = e-2 and A = $2 d2 dx2 , IS this function an eigenfunction of the A? If so, what is the eigenvalue? 5. If d = -,determine if the following function are eigenfunction of this operator, and if so, what is the eigenvalue: a. ae-3x + be-3ix b. cos(ax) C. e-ix d. sin (x) b. e. e-ix2 6. For two vectors: A = (5, -1,3) and B = (-1,1,6) calculate i) the magnitude of A and B , ii) the dot product between these two vectors, iii) the cross product between these two vectors, and iv) the magnitude of the vector produced by the cross product of these two vectors. 7. If z1 = 5 + i and z2 = -3 + 5i calculate i) Z1Z2, ii) Z1 + Z2, iii) z1/Z2, iv) ZiZ,*and v) ZzZz*