- #1
phil ess
- 70
- 0
Homework Statement
Assume there is a source of some pre-selected atoms. When measuring atoms of that source in a Stern-Gerlach, you find the following probabilities for a spin-up result:
x-direction 5/6
y-direction 5/6
z-direction 1/3
Which state would you ascribe to the source?
Homework Equations
?
The Attempt at a Solution
Let the atoms be:
[tex]\[ \left( \begin{array}{ccc}
\alpha \\
\beta \end{array} \right)\][/tex]
Decomposing in the z-basis we get that the probability amplitudes for up and down are [tex]|\alpha|^2[/tex] and [tex]|\beta|^2[/tex], respectively.
From this we find that [tex]\alpha = 1/\sqrt{3}[/tex] and [tex]\beta = \sqrt{2/3}[/tex]
Ok this is where I am confused, my textbook says we need to do a measurement in all 3 directions, but I got these values with just the z result?
If someone could explain this to me itd be a big help, I am stuck :(