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?

An isolated conducting spherical shell carries a positive charge. part a which statement (or statements) about the electric field and the electric potential inside and outside the spherical shell is correct? which statement (or statements) about the electric field and the electric potential inside and outside the spherical shell is correct? electric potential inside the shell is constant and outside the shell is changing as 1/r2 both the electric potential and the electric field does change with r inside and outside the spherical shell electric potential inside and outside the shell is constant, but not zero electric potential inside the shell is constant and outside the shell is equal to zero electric field inside and outside the shell is constant (does not change with the position r), but is not equal to zero electric field inside and outside the shell is changing as 1/r (where r is the distance from the center of the sphere) electric field inside is equal to zero and outside the shell is constant, but not zero electric potential inside the shell is constant and outside the shell is changing as 1/r electric field inside and outside the shell is changing as 1/r2 electric field inside is equal to zero and outside the shell is changing as 1/r2 electric field inside and outside the shell is zero electric field inside is constant and outside the shell is changing as 1/r