unit3000-21

135 reputation

	135 reputation	bio	website		visits	member for	1 year, 1 month
3 badges		location			seen	Jul 5 '12 at 1:33

11 Actions

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