# Electron spin

#### Grand

1. Homework Statement
Say we want to fiddle with spin of a particle.

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

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

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

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#### tiny-tim

Homework Helper
Hi Grand! If you multiply any eigenstate by an ordinary complex number, don't you get the same eigenstate?

#### Grand

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 $$s_z$$ to be 1/2 and -1/2 is 1 and for the same calculation, but for y it is i.

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