Stern-Gerlach Probability: Find the Probability

[cscott]

Homework Statement

We're learning some basic quantum mechanics by studying the stern-gerlach experiment so some of my terminology might be a bit off as it might be particular to this book, I'm not sure.

Say we have +z atoms (magnetic moment in +z direction?) shot through a +x selector followed by a -z selector. I need to find the probability that the atoms pass through.

Should I get probabilities 1/2 * 0 = 0. So 0 percent make it out?

What happened to that latex guide on here btw? I don't know how to make bras or kets or up/down arrows.

 

[dextercioby]

What's the initial state of the system ? Then what happens to it afterwards ?

 

[cscott]

The initial state would be $$|\uparrow_z>$$

Then there is an +x selection measurement so wouldn't 50% get filtered out?

Then the -z selector would block the 50% from the first measurement?

 

[Meir Achuz]

The initial state would be $$|\uparrow_z>$$

Then there is an +x selection measurement so wouldn't 50% get filtered out?
Then the -z selector would block the 50% from the first measurement?

No. After the x selector, the atoms are polarized in the x direction, but this means that half of those left will pass the z selector and be polarized in the z direction.
QM spin works like that.

 

[cscott]

So 50% of the +z atoms would get selected in the +x selection and be polarized in +x. Then another 50% of those +x atoms will get slected in the -z selector? Which means 25% would make it through in total?

 

[cscott]

Can anyone verify this reasoning?