• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Electron spin

  • Thread starter Grand
  • Start date
76
0
1. 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].
 

tiny-tim

Science Advisor
Homework Helper
25,790
247
Hi Grand! :wink:

If you multiply any eigenstate by an ordinary complex number, don't you get the same eigenstate?
 
76
0
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.
 

Related Threads for: Electron spin

  • Posted
Replies
8
Views
2K
  • Posted
Replies
2
Views
4K
  • Posted
Replies
2
Views
2K
Replies
1
Views
5K
  • Posted
Replies
6
Views
454
Replies
4
Views
889
  • Posted
Replies
1
Views
992
  • Posted
Replies
4
Views
10K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top