Asmall bead of mass m is attached to one end of a (thin, rigid, massless) bar of length r, while the other end of he bar is fixed in place but free to pivot, such that the bead rotates without friction in the (x, y) plane. for now neglecting gravitv, air resistance, etc.: (a) what are the allowed energy levels? in standard polar coordinates in the (x, y) plane, suppose the wavefunction for the bead at time t - 0 is given by cos (b) what possible values of angular momentum lz could be found in an ideal measurement? c) what is the probability of finding each such value? (d) what is the expectation value of l2? (e) what is the expectation value of lr? (f) what is the expectation value of ly? (g) what is the expectation value of the angular position φ of the bead? (h) starting with the wavefunction specified above. find the wavefunction џ'(d, t) of the bead at sub- sequent times in the absence of measurements up to time t. which answers, if any, to parts (b) - (e) would change if measurements are made at a time t > 0 than at t- 0?