What Is the Probability of Measuring Spin-up for Electron in State Alpha?

[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 probability is (<y+|alpha>)^2 . but in the solution i attached , the solution is different ! I'm confused !



thank you for your help

 

[Goddar]

Don't bother, your solution is correct.

 

[the_doors]

so the solution is incorrect ?

 

[Goddar]

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

 

[vela]

so the solution is incorrect ?

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 $\langle +_y \vert \alpha,\beta\rangle$.