A collection of spin-1 particles is prepared in the state (-) -2 5 |) = N " with the column vector written in the z-basis. Use the matrix representation for all calculations. (a) Find the normalization constant N. (b) Look up the normalized eigenstates of Sy and write them as column vectors in the z-basis. (c) What are the possible results of an Sy-measurement and their probabil- ities? (d) Calculate the expectation value and standard deviation for an Sy-measurement on this collection of particles.