Let n = (ex + ey + ez)/

3. Consider a sequential Stern-Gerlach(SG) experiment where the first SG setup is aligned along the z direction and the

|Sz, i beam is blocked and the |Sz, +i beam is sent into a second SG setup

aligned along the n direction. 1000 spins are prepared in the initial state

|bi =

1

2

(|Sz, +i +

3|Sz, i) and sent through the sequential SG setup as

shown in the figure below.

|bi Sz n S

|n S, +i beam

(a) Express the normalized state |n S, +i in the basis |Sz, i.

(b) On an average, how many spins will be observed in the |n S, +i beam.

Round your answer to the nearest integer.