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Consider an electron in an external 'magnetic field in the Sz$ - direction, $\mathbf{B} = B_z \hat{k}$. If the initial spin state of the electron is the eigenstate of SS_XS with eigenvalue S+\hbar/2$, \begin{enumerate} \item[a)] Find the state of the system at time St$. \item [b)] Show

Consider an electron in an external 'magnetic field in the Sz$ - direction, $\mathbf{B} = B_z \hat{k}$. If the initial spin state of the electron is the eigenstate of SS_XS with eigenvalue S+\hbar/2$, \begin{enumerate} \item[a)] Find the state of the system at time St$. \item [b)] Show

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Consider an electron in an external magnetic field in the SzS-direction, $\mathbf{B} B_z \hat{k}S. If the initial spin state of the electron is the eigenstate of SS_x$ with eigenvalue S+\hbar/2$, \begin{enumerate} \item[a)] Find the state of the system at time St$. \item [b)] Show that the system returns to its initial state and calculate the angular frequency. \item [c)] Calculates the expected value of SS_XS, SS_yS and SS_ZS as a function of time. \ end {enumerate}
Transcribed Image Text:Consider an electron in an external magnetic field in the SzS-direction, $\mathbf{B} B_z \hat{k}S. If the initial spin state of the electron is the eigenstate of SS_x$ with eigenvalue S+\hbar/2$, \begin{enumerate} \item[a)] Find the state of the system at time St$. \item [b)] Show that the system returns to its initial state and calculate the angular frequency. \item [c)] Calculates the expected value of SS_XS, SS_yS and SS_ZS as a function of time. \ end {enumerate}
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