This is a conceptual question that has to do with SG

[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?

 

[mfb]

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.

 

[D__grant]

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.

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...

 

[mfb]

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".

 

[D__grant]

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".

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!

 

[mfb]

Even though you're given an electron in Sz, and then put it through a magnetic field in the Z-direction, makes no difference?

No difference in which way?

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.

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

 

[D__grant]

No difference in which way?

-Well the electron's quantum #'s are in Sz, and our magnetic field is in the same axis. Don't you typically have an electrons quantum state in Sz, and send it through the Sx axis?


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

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

 

[mfb]

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