When the spin-orbit interaction is taken into account, an energy eigenstate of a hydrogen atom takes the form |a)= f(r)y3.1(0, 1) + g(r)y32(0,6)| 1), where yi, m is a spherical harmonic with angular momentum quantum number and magnetic quantum number m and f) and | ! ) are spin-up and spin-down eigenvectors relative to the z-axis (a) if l2 (the square of the orbital angular momentum) is measured in the state |a), what value of l2 will be obtained with certainty? explain your reasoning (b) if l (the z-component of the orbital angular momentum) is measured in the state |a), which two values of l can be obtained? explain your reasoning (e) if jl s. (the z-component of the total angular momentum) is measured in the state |a), what value of j will be obtained with certainty? explain your reasoning