Stern-Gerlach Probability: Find the Probability

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Homework Help Overview

The discussion revolves around the Stern-Gerlach experiment in quantum mechanics, specifically focusing on the probability of atoms passing through a series of measurement selectors. The original poster is uncertain about the terminology and calculations related to the probabilities of different spin states.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the initial state of the system and the effects of sequential measurements on the probabilities of passing through the selectors. Questions arise regarding the interpretation of the measurement outcomes and the implications of quantum spin behavior.

Discussion Status

There is an ongoing exploration of the reasoning behind the probabilities involved in the Stern-Gerlach experiment. Some participants are attempting to clarify the effects of the +x and -z selectors on the initial +z state, while others are questioning the assumptions made about the outcomes.

Contextual Notes

The original poster expresses confusion about terminology and the use of quantum notation, indicating a potential barrier to fully engaging with the problem. There is also a mention of a missing latex guide, which may affect the clarity of mathematical expressions in the discussion.

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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.
 
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What's the initial state of the system ? Then what happens to it afterwards ?
 
The initial state would be [tex]|\uparrow_z>[/tex]

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?
 
cscott said:
The initial state would be [tex]|\uparrow_z>[/tex]

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.
 
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?
 
Can anyone verify this reasoning?
 

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