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

A spin 1/2 particle is in the state [tex]\left| \Psi \right\rangle[/tex] = [tex]\sqrt{2/3}\left|\uparrow\right\rangle + i\sqrt{1/3}\left|\downarrow\right\rangle[/tex]

A measurement is made of the x-component of the spin. What is the probability that the spin will be in the -x direction?

2. Relevant equations

Spin states are represented as linear combinations of the spin in the +z direction and -z direction, since these spins form an orthonormal basis set:

http://en.wikipedia.org/wiki/Spin-½#Mathematical_description

In this case, spin in -x direction is represented by

[tex]\sqrt{1/2} \[

\left( {\begin{array}{cc}

1 \\

-1 \\

\end{array} } \right)

\][/tex]

3. The attempt at a solution

P = [tex]\left|\left\langle\leftarrow\left|\Psi\right\rangle\left|^{2}[/tex]

= the transpose of the [tex]\leftarrow[/tex] matrix, times the [tex]\Psi[/tex] matrix, squared.

When calculating this straightforwardly, I will end up with a complex probability because of the i term in the [tex]\Psi[/tex] matrix. That doesn't make sense!

So, do I just take this complex number and find its magnitude in the complex plane, and then square that?

Or something else?

Thanks!

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# Homework Help: The probability that spin will be in -x direction!

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