# Homework Help: This is a conceptual question that has to do with SG

1. Dec 15, 2012

### D__grant

This is a conceptual question that has to do with SG devices:

You're given amplitudes for an electron for Sz. What will happen if that same electron is passed through a Z-apparatus? And then one in the x-direction?

From my understanding the electron then has equal probabilities of spin up & spin down after the Z-apparatus, but the fact that amplitudes were first given in Sz & then were shot through a SG apparatus in the Sz direction confuses me.

Any insight?

2. Dec 15, 2012

### Staff: Mentor

Re: Stern-Gerlach

Amplitudes for "up" and "down"? Then you can calculate the probabilities based on those amplitudes. 0.5 for both directions is just a special case.

3. Dec 15, 2012

### D__grant

Re: Stern-Gerlach

An electron has an amplitude of 0.8 for Sz = +hbar/2 and
an amplitude of 0.6 for Sz ==-hbar/2.

- What is the probability that if we send it into a Stern-Gerlach device with its magnetic field in the z direction, it will emerge in the Sz = +hbar/2 beam?

-If it does emerge in Sz = +hbar/2 beam,
and we then send it through a Stern Gerlach machine with its field in the x direction, what is the probability that it will emerge in the Sx = +hbar/2 beam?
--
I was under the impression SG devices work like polarizers...

4. Dec 15, 2012

### Staff: Mentor

Re: Stern-Gerlach

They work similar to them.

You can use the Born rule to convert amplitudes to probabilities.
This is a fancy way to say "square them and take the absolute value".

5. Dec 15, 2012

### D__grant

Re: Stern-Gerlach

Is this question really that straight forward? Even though you're given an electron in Sz, and then put it through a magnetic field in the Z-direction, makes no difference? I'm sorry I just thought that the Z-apparatus would only allow either spin up or spin down electrons based on their previous amplitudes.

Thank you! I need this help!!

6. Dec 15, 2012

### Staff: Mentor

Re: Stern-Gerlach

No difference in which way?

Each electron is either measured as up or down, right.

7. Dec 15, 2012

### D__grant

Re: Stern-Gerlach

No, I know each electron can be measured either spin up or spin down, i'm asking what this Z-apparatus does to an electron with this quantum state

8. Dec 15, 2012

### Staff: Mentor

Re: Stern-Gerlach

With the Copenhagen interpretation, it will collapse it into either up or down.