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\centerline{\bf System of two spin-$\frac{1}{2}$ particles}
\bigskip

\underline{Small white board questions:}

\begin{enumerate}
\item The electron has spin $\frac{1}{2}$, with spin up and spin down eigenstates $\vert \pm \rangle_{e}$.
For the electron, use the symbol $S$ for the spin $S_{e}$.


Write down the eigenvalue equations for the electron states.


\item The proton has spin $\frac{1}{2}$, with spin up and spin down eigenstates $\vert \pm \rangle_{e}$.
For the proton, use the symbol $I$ for the spin $S_{p}$.

\item	Write down the eigenvalue equations for the proton states.


\item The system of electron and proton could be in the state:
$$
\vert e^{-} \: up \rangle \vert p^{+} \: up \rangle = \vert + \rangle_{e} \vert + \rangle_{p} \equiv \vert + + \rangle
$$
 
 
Using the compact $\vert + + \rangle$ notation, what are the possible spin states of the electron-proton system?
\end{enumerate}

\underline{Large white board activities:}

\begin{enumerate}
\item	Find the matrix representation of the electron spin component operator $S_{z}$ .


\item	Find the matrix representation of the proton spin component operator $I_{z}$.
\end{enumerate}

\vfill 
\leftline{\textit{ by David McIntyre}}
\leftline{copyright DATE David McIntyre}

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