Suppose we have an proton (a spin21 particle), initially in the |z state. The proton has charge e, mass m, and gyromagnetic moment >0. What we really want though, for our new experiment, is a proton oriented in such a way that when we measure the spin of the proton along the direction n^=21(x^+y^), we always end up measuring /2.

Luckily we're able to apply magnetic fields, which can rotate an proton's spin vector.

However, we're only able to apply magnetic fields of strength B₀ along one of the x^,y^ orz^ directions, but we can apply a magnetic field for however we want, and we can also apply different magnetic fields in a sequence (for example, we could applyB1=B0z^ for one second, thenB2=B0x^ for three seconds, then another field, etc... but neverB4=B0(2x^+y^) or B5=2B0z^)

Describe a short sequence of magnetic fields we could apply so that we get an proton definitely in the state |n.