Assume that the |+z) and |−z) states for an electron in a magnetic field are energy eigen- vectors with energies E and 0, respectively, and assume that the electron's state at t = 0 is |y(0)) = = 1+110-14 M Find the probability that we will determine this electron's spin to be in the +x direction at time t

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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 \(t\).
Transcribed Image Text: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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