Suppose that at time $t=0$ an electron in a magnetic field in the $+z$ direction has state $|\psi(0)\rangle=|+x\rangle$. Let $\omega=\left[E_{+}-E_{-}\right] / \hbar$.
-(a) The expectation value $\left\langle s_{z}\right\rangle$ as a function of time in this case is which of the below?
A) $+\frac{1}{2} \hbar$
B) $-\frac{1}{2} \hbar$
C) 0
D) $+\frac{1}{2} \hbar \cos \omega t$
E) $+\frac{1}{2} \hbar \sin \omega t$
F) Something else (specify)

Question

Quizplus · Accepted Answer

The expectation value $\left\langle s_{z}\right\rangle$ of an electron initially in the state $|+x\rangle$ and subjected to a magnetic field in the $+z$ direction evolves in time as $+\frac{1}{2} \hbar \cos \omega t$. This is because the state $|+x\rangle$ can be expressed as a superposition of $|+z\rangle$ and $-z\rangle$ states, and the time evolution introduces a phase difference between these components that varies as $\cos \omega t$, leading to the given expectation value for $\left\langle s_{z}\right\rangle$.

Suppose That at Time t=0t=0t=0 An Electron in a Magnetic Field in The

Suppose That at Time $t=0$ An Electron in a Magnetic Field in The