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Assume that the \(|+z\rangle\) and \(|-z\rangle\) states for an electron in a magnetic field are energy eigenvectors with energies \(E\) and \(0\), respectively, and assume that the electron’s state at \(t = 0\) is

\[
|\psi(0)\rangle = \begin{bmatrix} \sqrt{\frac{4}{5}} \\ \sqrt{\frac{1}{5}} \end{bmatrix}
\]

Find the probability that we will determine this electron’s spin to be in the \(+x\) direction at time \(t\).

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