- #1
crowlma
- 8
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Homework Statement
What is the expectation value of [itex]\hat{S}_{x}[/itex] with respect to the state [itex]\chi = \begin{pmatrix}
1\\
0
\end{pmatrix}[/itex]?
[itex]\hat{S}_{x} = \frac{\bar{h}}{2}\begin{pmatrix}
0&1\\
1&0
\end{pmatrix}[/itex]
Homework Equations
[itex]<\hat{S}_{x}> = ∫^{\infty}_{-\infty}(\chi^{T})^{*}\hat{S}_{x}\chi[/itex]
The Attempt at a Solution
So I have [itex](\chi^{T})^{*}[/itex] as equalling (1 0), giving me: [itex]\frac{\hbar}{2} ∫^{\infty}_{-\infty}\begin{pmatrix}
1&0
\end{pmatrix}\begin{pmatrix}
0&1\\
1&0
\end{pmatrix}\begin{pmatrix}
1\\
0
\end{pmatrix} [/itex] which simplifies to [itex]\frac{\hbar}{2} ∫^{\infty}_{-\infty}\begin{pmatrix}
1&0
\end{pmatrix}\begin{pmatrix}
1\\
0
\end{pmatrix} = 0 [/itex]. Is this right?