Imagine that an electron with an initial spin state
$$|\psi\rangle=\left[\begin{array}{c}
\frac{3}{5} \
-\frac{4}{5}
\end{array}\right]$$
Goes into an SGx device and comes out the - channel of that device. The electron's spin state is now
A) $\left[\begin{array}{l}\sqrt{1 / 2} \ \sqrt{1} / 2\end{array}\right]$
B) $\left[\begin{array}{l}-\sqrt{1 / 2} \ -\sqrt{1 / 2}\end{array}\right]$
C) $\left[\begin{array}{l}\sqrt{1 / 2} \ -\sqrt{1 / 2}\end{array}\right]$
D) $\left[\begin{array}{l}1 \ 0\end{array}\right]$
E) $\left[\begin{array}{l}0 \ 1\end{array}\right]$

Question

Quizplus · Accepted Answer

The SGx device measures the spin along the x-axis. The eigenstates for spin along the x-axis are $\frac{1}{\sqrt{2}}\left[\begin{array}{c}1 \ 1\end{array}\right]$ for the + channel and $\frac{1}{\sqrt{2}}\left[\begin{array}{c}1 \ -1\end{array}\right]$ for the - channel. Since the electron comes out the - channel, its state is aligned with the - eigenstate, which matches choice C.

Imagine That an Electron with an Initial Spin State ∣ψ⟩=[35−45]|\psi\rangle=\left[\begin{array}{c}\frac{3}{5} \\-\frac{4}{5}\end{array}\right]∣ψ⟩=[53​−54​​]

Imagine That an Electron with an Initial Spin State $|\psi\rangle=\left[\begin{array}{c}\frac{3}{5} \\-\frac{4}{5}\end{array}\right]$