I've got a question. Let's say I've got a linear combination of spherical harmonics with respect to some coordinate system. How do perform a change of basis into another coordinate system? I thought of using the rotation operator on the basis states (the old spherical harmonics), but I don't know how the rotation operator acts on these states...and to know how they act on these states I feel like I'd need to know what the new states are in the first place

...which is what i'm trying to figure out

@PM2Ring thanks, good catch.

Just woke up and Alexa told me in Germany you can't walk hugging a pillow

I found this question and I completely agree with the accepted answer. What worries me is that I've run into that "abstract" group stuff and "$\mathrm{SO(3)}$ is a representation of the rotation group" in different (possibly unrelated) sources. So I'm wondering if this is a common misconception

Should I be flagging stuff like this as Very low quality? physics.stackexchange.com/a/740324/123208 This guy has been a member for a few months and has posted a lot of poor answers. Sometimes they contain obvious errors, but mostly the grammar & sentence structure is so bad that it's hard to tell what he's trying to say. In either case, I feel that a downvote is justified, since incoherent answers are not useful.

Frankly, I'm a little surprised that he hasn't been answer-banned. Maybe a mod can have a quiet word with him...

Hi All...

What is the correct definition of pressure?

1. Force exerted on area

2. Force equally distribute over the entire area

3. Force feel by the entire area.

4. Force acting per unit area

@123 According to ISO, pressure $p$ is defined as $p=\mathrm dF/\mathrm dA$, where $\mathrm dF$ is the force component perpendicular to the surface element of area $\mathrm dA$.

@Feynman_00 what is the misconception?

@SillyGoose Take a look at the last paragraph of the accepted answer

@Feynman_00 never heard of this but who knows

@NiharKarve To be honest I don't remember where I heard it but also other people I know apparently knew this version

@Feynman_00 physicists are bad at group theory, and they often get sloppy about the difference between groups being isomorphic and their complex projective representation theory being the same; e.g. You can find statements in Zee that the Lorentz group is isomorphic to SU(2)xSU(2), this sort of confusion is not uncommon

@PM2Ring I just received the comment Try pyAutoLens library

If I'm feeling brave I may try to install it pyautolens.readthedocs.io/en/latest

@ACuriousMind So there is no "abstract" rotation group at all? Just $\mathrm{SO}(3)$ (which is a matrix Lie group) being the rotation group