Spring 2006 5 Qm

Spring 2006

Spring 2006 1 Mech
Spring 2006 2 Mech
Spring 2006 3 EM
Spring 2006 4 EM
Spring 2006 5 QM
Spring 2006 6 QM
Spring 2006 7 SM
Spring 2006 8 SM
Spring 2006 9 Misc
Spring 2006 10 Misc
Spring 2006 11 Mech
Spring 2006 12 Mech
Spring 2006 13 EM
Spring 2006 14 EM
Spring 2006 15 QM
Spring 2006 16 QM
Spring 2006 17 SM
Spring 2006 18 SM
Spring 2006 19 Misc
Spring 2006 20 Misc

A proton (spin - 1/2 ) is in the spin state

(1)

\begin{align} \chi=\frac{1}{4}\left( \begin{array}{c} 2 - 3 \imath \\ \imath \sqrt{3} \\ \end{array} \right) \end{align}

where the spinor corresponds to the representation where, e.g., the state with spin up along the z-axis is

(2)

\begin{align} \chi_+ = \left( \begin{array}{c} 1\\ 0\\ \end{array} \right) \end{align}

(a) What is the expectation value for the angular momentum operator in the z-direction?

(b) What is the expectation value for the angular momentum operator in the x-direction?

(c) What is the expectation value for the angular momentum operator in the y-direction?

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Answer

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