unit3000-21
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 Sep 29 awarded Autobiographer May 7 awarded Supporter May 7 accepted Eigenvalue of $L_z$ May 7 comment Eigenvalue of $L_z$ Ah, you're absolutely right. This is my fault: I was looking for justification in the pages before, not the pages after. The very next page describes exactly what you said. Thanks. May 6 comment Eigenvalue of $L_z$ If it helps, you could just ignore my last sentence. In that case, I'm just wondering what allows us to claim that $\hbar \ell$ is an eigenvalue of $L_z$. In the text, this is stated and not justified (as far as I can tell). May 6 asked Eigenvalue of $L_z$ Apr 23 awarded Scholar Apr 23 accepted Electric dipole transitions/expectation value of position Apr 23 comment Electric dipole transitions/expectation value of position You're not missing anything, it really is that simple! However, I couldn't flesh out the details until late last night. I ended up converting to Cartesian coordinates, in which case $\Psi^\ast \Psi$ is even in each of $x,y$ and $z$ since $r \mapsto \sqrt{x^2+y^2+z^2}$. Thus, $\Psi^\ast x \Psi$ is odd in $x$, and similarly for $y$ and $z$. So the integral of each is zero, which means the integral of the original thing is zero. Apr 23 awarded Student Apr 22 comment Electric dipole transitions/expectation value of position Can someone fix the box after the $r$? I used \vec{} but as I usually do, but it apparently did not render here. Apr 22 asked Electric dipole transitions/expectation value of position