1.(a) Consider a complex vector space where kets are represented as three dimensional column vectors with respect to the orthonormal basis 2 2) = OHO and *3) = A certain Hermitian linear operator H has a matrix representation with respect to this basis of 1/2 2 H = -i 2 Calculate the eigenvalues and corresponding orthornormal eigenvectors of this operator. Construct a unitary transformation that diagonalizes H, and carry out that diagonalization explicitly. (b) With respect to the new basis of eigenvectors of H, calculate the matrix representations of the vector (x) and operator A, which have matrix representations in the old basis of O E = O and A = 0 respectively