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seen Aug 28 at 3:00

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