(c) You select one of the beams from part b above, and pass it through another magnetic field in the z-direction. Does the beam split? If so, what fraction of the particles go to each side? Compare with part a and explain. 2 sics 137A, Spring 2022 Homework 8 Due Friday, 15 April spin up beam spin down Figure 1: The Stern-Gerlach experiment (d) Suppose we start with N particles. We first pass them through a magnetic field in the z-direction, and block the beam that goes down. After this process, you find that only particles remain. They then go through a magnetic field in the a-z plane, an angle 0 from the z-axis, and the beam that goes against the direction of the field is blocked. Then you have a magnetic field in the z-direction again, and block the beam that goes up this time. How many particles come out? Compare with the case without the middle magnetic field.
(c) You select one of the beams from part b above, and pass it through another magnetic field in the z-direction. Does the beam split? If so, what fraction of the particles go to each side? Compare with part a and explain. 2 sics 137A, Spring 2022 Homework 8 Due Friday, 15 April spin up beam spin down Figure 1: The Stern-Gerlach experiment (d) Suppose we start with N particles. We first pass them through a magnetic field in the z-direction, and block the beam that goes down. After this process, you find that only particles remain. They then go through a magnetic field in the a-z plane, an angle 0 from the z-axis, and the beam that goes against the direction of the field is blocked. Then you have a magnetic field in the z-direction again, and block the beam that goes up this time. How many particles come out? Compare with the case without the middle magnetic field.
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please answer c and d
Transcribed Image Text:5. Measuring Spin
Imagine you have a beam of spin 1/2 particles moving in the y-direction. We can set up an
inhomogeneous magnetic field to interact with the particles, separating them according to
their spin component in the direction of the magnetic field, B-S. This is the Stern-Gerlach
experiment, depicted in Fig. 1.
(a) You set up a magnetic field in the z-direction. As the beam of particles passes
through it, it splits in two equal beams: one goes up, corresponding to the spin-up
particles (those whose S, eigenvalue was +), and the other goes down, correspond-
ing to the spin-down particles. Now, you take the beam that went up and pass it
through another magnetic field in the z-direction. Does the beam split? If so, what
fraction of the particles go to each side?
(b) Instead, you pass the beam through a z-field, take the beam that went up, and pass
it through a magnetic field in the x-direction. Does the beam split? If so, what
fraction of the particles go to each side?
(c) You select one of the beams from part b above, and pass it through another magnetic
field in the z-direction. Does the beam split? If so, what fraction of the particles go
to each side? Compare with part a and explain.
2
Physics 137A, Spring 2022
Homework 8
Due Friday, 15 April
spin up
beam
spin down
そ
Lay
Figure 1: The Stern-Gerlach experiment
(d) Suppose we start with N particles. We first pass them through a magnetic field in
the z-direction, and block the beam that goes down. After this process, you find
that only particles remain. They then go through a magnetic field in the x-z
plane, an angle 0 from the z-axis, and the beam that goes against the direction of
the field is blocked. Then you have a magnetic field in the z-direction again, and
block the beam that goes up this time. How many particles come out? Compare
with the case without the middle magnetic field.
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