The Hamiltonian of a 2-level system is given by = hw (1 2) where w is a constant with a dimension of frequency. Suppose that a particle in the system has an initial wave function of |, 0) = A (). At a later time t, a measurement of energy is performed on this particle. (a) Find all possible results of the energy measurement. (b) Calculate the probability to obtain each of the result at time t. (c) Check whether operator = W v (2 1) represents a conserved quantity in this 2-level system. (d) Suppose that an operator Q = q (0; 1) is 9 (0; 1) is in the linear space spanned by the eigenvectors of . -i Rewrite in the linear space spanned by the eigenvectors of Q.