# Sakurai chapter 3, Problem 1.

1. Feb 12, 2014

### the_doors

hello guys

Suppose an electron is in the spin state alpha=(a,b). if s_y is measured, what is the probability of result h/2 ?

s_y eigenvector for +h/2 is |y+>=1/sqrt(2) (1,i)) so the probabilty is (<y+|alpha>)^2 . but in the solution i attached , the solution is different ! i'm confused !

thank you for your help

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2. Feb 12, 2014

### Goddar

Don't bother, your solution is correct.

3. Feb 12, 2014

### the_doors

so the solution is incorrect ?

4. Feb 12, 2014

### Goddar

well there's certainly something wrong when you measure a probability in terms of $\hbar$2...

5. Feb 12, 2014

### vela

Staff Emeritus
Yes, the solution is incorrect. Whoever wrote it made the common mistake of conflating making a measurement with applying the associated operator. In other words, the "solution" calculates $\langle +_y \lvert \hat{S}_y \rvert \alpha,\beta\rangle$ for the probability amplitude while you correctly calculated $\langle +_y \vert \alpha,\beta\rangle$.

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