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?

The following statements are about the electroscope. select all that are true. if an electroscope were given a positive charge beforehand, the leaves would move closer together if a positively charged object were brought near. when a properly prepared electroscope is used to determine the type of charge on an object, the total charge on the electroscope changes when the charged object is brought near (but not touching) the electroscope. depending on how the electroscope is prepared beforehand, the leaves can either move together or move apart when negative charge is brought near. an electroscope must first be given a known type of charge before it can be used to identify the types of charges on objects brought near it. when properly prepared, the leaves on an electroscope will always move further apart when negative charge is brought near. the leaves of an electroscope will move apart if it is given either a positive or a negative charge.