- #1

happyparticle

- 400

- 20

- Homework Statement
- Probabilities of measuring ##\pm \hbar/2## along ##\hat{n}##?

- Relevant Equations
- ##|+\rangle_n = cos(\theta/2)e^{-i\phi/2}|+\rangle +sin(\theta/2)e^{i\phi/2}|-\rangle##

##|-\rangle_n = sin(\theta/2)e^{-i\phi/2}|+\rangle -cos(\theta/2)e^{i\phi/2}|-\rangle##

Hi,

Given a spin in the state ##|z + \rangle##, i.e., pointing up along the z-axis what are the probabilities of measuring ##\pm \hbar/2## along ##\hat{n}##?

My problem is that I'm not sure to understand the statement. It seems like I have to find the probabilities of measuring an eigenvalue along ##\hat{n}##. What does that mean exactly? Is it the probability to measure ##\pm \hbar/2## in the ##n## basis?

I tried to find ## |+\rangle ## in the ##n## basis, which I think this is ##|z+\rangle## in the ##n## basis. I thought maybe it could help me.

I got ## |+\rangle = 1/2 (cos (\theta/2) e^{i\theta /2} |+ \rangle_n + sin (\theta/2)e^{i\theta /2} |- \rangle_n)##

I'm really confuse with this statement. I'm not sure to understand the difference between ##|z + \rangle## and ##|+\rangle##

Given a spin in the state ##|z + \rangle##, i.e., pointing up along the z-axis what are the probabilities of measuring ##\pm \hbar/2## along ##\hat{n}##?

My problem is that I'm not sure to understand the statement. It seems like I have to find the probabilities of measuring an eigenvalue along ##\hat{n}##. What does that mean exactly? Is it the probability to measure ##\pm \hbar/2## in the ##n## basis?

I tried to find ## |+\rangle ## in the ##n## basis, which I think this is ##|z+\rangle## in the ##n## basis. I thought maybe it could help me.

I got ## |+\rangle = 1/2 (cos (\theta/2) e^{i\theta /2} |+ \rangle_n + sin (\theta/2)e^{i\theta /2} |- \rangle_n)##

I'm really confuse with this statement. I'm not sure to understand the difference between ##|z + \rangle## and ##|+\rangle##