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Basic Probability question for a spin 1/2 Particle

  • Thread starter richyw
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Homework Statement



A beam of spin-1/2 particles is prepared in the state

[tex]\left|\psi\right\rangle=\frac{2}{\sqrt{13}}\left|+\right\rangle_x+i \frac{2}{\sqrt{13}}\left|-\right\rangle_x[/tex]

a) What are the possible results of a measurement of the spin component Sz, and with what probabilities would they occur?

b) What are the possible results of a measurement of the spin component Sx, and with what probabilities would they occur?

Homework Equations



[tex]P_x=\left|\left\langle x\right| \left. \psi \right\rangle\right|^2[/tex]

The Attempt at a Solution



So I can find out the answer to part b just by plugging it straight into the formula and using that [itex]_x\left\langle +\right| \left. + \right\rangle_x=1[/itex] and [itex]_x\left\langle +\right| \left. - \right\rangle_x=0[/itex]

my problem is with the first part of the question. If I use the same method as before I end up with
[tex]_z\left\langle +\right| \left. + \right\rangle_x\\
_z\left\langle +\right| \left. - \right\rangle_x\\
_z\left\langle -\right| \left. + \right\rangle_x\\
_z\left\langle -\right| \left. - \right\rangle_x[/tex] in my equations. And I do not understand how to know what these are.
 

Answers and Replies

  • #2
34,264
10,308
You can express ##_z\left\langle +\right |## in terms of ##_x\left\langle +\right |## and ##_x\left\langle -\right |## (or vice versa).

Your wavefunction does not look properly normalized.
 

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