Mechanics of Stern-Gerlach Experiments Question.

In summary, the conversation discusses an experiment where a magnetic field was placed along the y and z axis. The equation for the state of spin +Y, +Z, and -Z with probability amplitudes a and b was written. The equation was then modified by taking the bra < +Z| and solving for it. The original equation was also modified to include the state of spin +Z with probability amplitude b. The conversation concludes with the question of why the modified equation is necessary, but the question is later resolved.
  • #1
Black Integra
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In an SGY-SGZ experiment, where the magnetic field were placed along the y and z axis,
we could write the equation:

[URL]http://bit.ly/pSN1u2[/URL]

for state of spin +Y, +Z, -Z respectively with the prob amplitudes a and b.

take the bra [itex]\left\langle +Z\right|[/itex] to the eq:

[URL]http://bit.ly/qugX1b[/URL]

thus
[URL]http://bit.ly/qg2K32[/URL]
also
[URL]http://bit.ly/qKXI5O[/URL]

so we have
[URL]http://bit.ly/oxzLXT[/URL]

But why the equation really is:
[URL]http://bit.ly/r3jcee[/URL]

Can anyone explain this to me?
 
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  • #2
ok sorry guys, problem is solved. my fault.
 

1. What is the purpose of the Stern-Gerlach experiment?

The Stern-Gerlach experiment is used to demonstrate the quantization of angular momentum in subatomic particles, specifically in electrons. This experiment helped to provide evidence for the existence of electron spin and its quantized nature.

2. How does the Stern-Gerlach experiment work?

In the Stern-Gerlach experiment, a beam of particles, usually silver atoms, is passed through a magnetic field. The atoms are deflected either up or down depending on their spin orientation. This deflection is due to the quantized nature of electron spin, which has only two possible orientations: up or down.

3. What are the implications of the Stern-Gerlach experiment?

The Stern-Gerlach experiment provided evidence for the quantization of angular momentum in subatomic particles, which is a fundamental property of quantum mechanics. It also led to the development of the concept of spin and its role in determining the behavior of subatomic particles.

4. How did the Stern-Gerlach experiment contribute to the development of quantum mechanics?

The Stern-Gerlach experiment played a crucial role in the development of quantum mechanics by providing evidence for the quantization of angular momentum and the existence of electron spin. This experiment also demonstrated the probabilistic nature of subatomic particles, which is a fundamental principle in quantum mechanics.

5. Can the Stern-Gerlach experiment be used to study other particles besides electrons?

Yes, the Stern-Gerlach experiment can be used to study other subatomic particles that have spin, such as protons, neutrons, and other atomic nuclei. It can also be used to study particles with half-integer spin, such as quarks, which play a crucial role in the Standard Model of particle physics.

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