If angular momentum is quantised (can only occur in discrete multiples of some value), what happens if you look at the same situation from a different point of view (frame of reference?). Wouldn’t this change the angular momentum values so they are no longer multiples of the particular value?
From whose point of view are the values quantised?
Apologies if the question doesn’t make sense …
First of all, angular momentum is quantized only for bound states or intrinsic angular momentum. Consider the angular momentum of an electron bound in a hydrogen atom. It has intrinsic angular momentum (spin), angular momentum associated with its bound state (the angular momentum you would measure in a lab at rest with respect to the atom and not counting spin), and any angular momentum associated with your relative position and velocity. The latter, like the energy of a free particle is not quantized.
To get a different angular momentum, you’d have to go to a rotating reference frame, but rotating reference frames can be distinguished with respect to the laws of physics.
Angular momentum is only quantized in systems with the appropriate properties (e.g. symmetry) such that l is a good quantum number, i.e. all the states of the system are eigenfunctions of the angular momentum operator. This is not true in relativistic systems, for example. I’m not as sure about the rotating frame argument, though – for one thing, how do you ever have a rotating frame corresponding to fractional hbar?
As an aside, a really interesting example of angular momentum in quantum systems is Bose-Einstein condensates with vortices in them. This Nature article demonstrates this really clearly.
Thanks for the great replies.
I think I even understood them! Angular momentum is basically not always quantized which I didn’t realise.
Well, in any context where you can measure angular momentum, it’s quantized, at least.