3
$\begingroup$

I'm given a spin state: $|s\rangle$ = some linear combination of $|\uparrow\rangle + |\downarrow\rangle$ possibly with an imaginary component.

$\hat{\mu}_e = g\mu_B\hat{\sigma}$

$g$ is the gyrmoagnetic factor and is approximately 2.0023.

$\mu_B =\frac{e\hbar}{2m_o}$ is the Bohr magneton.

I'm asked to find the expectation value of the electron spin magnetic moment. Which I believe is $\langle s| \hat{\mu}_e |s\rangle$

Yet the problem states that "Note: the result is a vector"

How and why would an expectation value be a vector?

$\endgroup$
1
$\begingroup$

In that case, $\hat{\sigma}$ here refers to a vector formed by $\hat{\sigma}_x$, $\hat{\sigma}_y$ and $\hat{\sigma}_z$ as its Cartesian components. The individual components of the expectation value of the magnetic moment vector would then be obtained using the corresponding components of the Pauli spin operators.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.