Mechanics of Stern-Gerlach Experiments Question.

[Black Integra]

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 $\left\langle +Z\right|$ 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?

 

[Black Integra]

ok sorry guys, problem is solved. my fault.