Let it'"(r) denote a simultaneous eigenfunction of the angular momentum operators l2 and lz. the respective eigenvalues are l(+1)ћ2 and тћ, with l a nonnegative integer and m =-1,-i + 1, . . , i (a) an atom is prepared with wavefunction consider separately measurements of l and lz. (i) what are the possible results of the measurement in each case? (ii) with what probability does each result occur? (b) a beam of atoms prepared in state v(r) enters a region of uniform magnetic field ib oriented in the r direction. the potential energy of interaction between each atonm and the magnetic field yields hamiltonian where is a constant. what is the state of an atom after it has spent a time t in the magnetic field? (c) the beam leaves the region of uniform field after a time t and the z-component of angular momentum is measured. for what proportion of the atoms is the result obtained?