Thanks for these replies. However, at least to me, they don't appear to answer my original question. I'm wondering if there is an intuitive explanation for the fact that it's possible to know the angular momentum precisely (equal to 0) and also know the orientation with a finite variance...
Thanks for sticking with this problem. Regarding the integral, it produces the same result independent of the domain of integration. The important thing is that the variance is the integral over the squared difference between the value and the mean of the value. The mean is necessarily going...
You're correct that you didn't say that the uncertainty relation would hold for the transformed variables. But then, why would I want to transform them? My entire question was about the uncertainty relation, so there's no point in doing transformations that break that relationship.
Also, I...
Thank you to both of your for your replies. I'm starting to come around to your view, but am still confused.
First, mfb wrote that if I don't like the finite angle interval, then I could just transform it to some other function without changing the physics. I don't agree with this because the...
Thanks for your reply. I agree with your comment about the 3D aspect, so perhaps I should have been more careful and said that I know that the orientation is within 0 and π on the θ coordinate and within 0 and 2π on the Φ coordinate. However, that doesn't fundamentally change the problem.
I...
I'm trying to understand the rotations of rigid diatomic molecules such as HCl. My understanding of the orbital angular momentum is that it is quantized with a total value equal to
$$E=\frac{\hbar^2}{2I}J(J+1)$$
where I is the rotational moment of inertia and J is the quantum number. Also, J...