(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

?

3. 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 Im 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, im stuck :(

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# Quantum State Tomography

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