Electron spin

  • Thread starter Grand
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  • #1
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Homework Statement


Say we want to fiddle with spin of a particle.

The state in which a measurement of [tex]s_x[/tex] is certain to yield +1/2 is:
[tex]|+,x\rangle=\sin{\frac{\pi}{4}}e^{i 0}|-\rangle+\cos{\frac{\pi}{4}}e^{-i 0}|+\rangle=\frac{1}{\sqrt{2}}(|-\rangle+\+|+\rangle)[/tex]

Now, for this state, we want to find the amplitude for measuring [tex]s_z[/tex] to be either 1/2 or -1/2. We have to apply the bra
[tex]\langle+,s_z|=sin0e^{i\phi/2}\langle-|+cos0e^{i\phi/2}\langle+|[/tex]

What I want to ask about is why in here [tex]\phi=0[/tex] as well - it is the z direction, which is determined only by [tex]\theta=0[/tex].
 

Answers and Replies

  • #2
tiny-tim
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Hi Grand! :wink:

If you multiply any eigenstate by an ordinary complex number, don't you get the same eigenstate?
 
  • #3
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Yes, we do. The probability is computed as mod squared of the amplitude. But here we have to show that the ratio of the complex amplitudes to measure the momentum [tex]s_z[/tex] to be 1/2 and -1/2 is 1 and for the same calculation, but for y it is i.
 

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