1. Consider a spin 1/2 particle. Call its spin S, its orbital angular momentum L and its state vector w ). The two functions v , (r) and w _ (r) are defined by : 4 + (r ) = Assume that : - i/ + (r) = R(r) Yo(0, Q) + Yo(0, Q) 3 R(r) 1_(r) = [Y)(0, 4) - Yi(0, 4)] where r, 0, p, are the coordinates of the particle and R(r) is a given function of r. a. What condition must R(r) satisfy for | y ) to be normalized ? b. S, is measured with the particle in the state | y ). What results can be found, and with what probabilities ? Same question for L., then for S.. C. A measurement of L', with the particle in the state | y ), yielded zero. What state describes the particle just after this measurement? Same question if the measurement of L had given 242