 #1
happyparticle
 369
 19
 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 zaxis 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 zaxis 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##