1. The Hamiltonian of a photon system is given as: H = aJ, + 2wh(=) (=] + ly)(#)). where a and w are constants, J, is the z component of the photon spin, (x) and ly) are the plane polarization states along the x and y axes respectively. At the initial instant, 1 = 0 the state is: |4(0)) = = (1i|:) + 3ly)) - What values can be obtained and with what probabilities when measuring the component z of angular momentum? " Write the matrix / in the basis [[R), [2)], which represents the right and left circular polarization respectively . if a = 0, what is the state of the system for a time t and what is the probability of finding a photon with right circular polarization