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While I am learning Quantum Mechanics with angular momentum and the two types of them:

  • orbital angular momentum

  • and internal angular momentum a.k.a. spin

  • (and total angular momentum, but that is a combined version).

So,

Is there any other types of angular momentum that does not recorded in textbooks or common literature?

PS. I am just talking about angular momentum in general Physics

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  • $\begingroup$ Vorticity. Quantum vortices are observed in nuclear physics and in superconductors. $\endgroup$ – ZeroTheHero Apr 21 '17 at 15:42
  • $\begingroup$ @ZeroTheHero How is that different from orbital angular momentum? $\endgroup$ – Emilio Pisanty Apr 21 '17 at 15:46
  • $\begingroup$ @EmilioPisanty I'm not too sure what the question means so my comment may not be applicable, but basically it's applicable to non-rigid bodies so it's neither intrinsic spin nor orbital angular momentum. Think of a bucket rotating about its axis: the water in it doesn't need to rotate at the same angular velocity as the bucket. $\endgroup$ – ZeroTheHero Apr 21 '17 at 15:48
  • $\begingroup$ @ZeroTheHero The vorticity in a superconductor boils down to a phase gradient of the wavefunction of a quantum particle which has a nonzero integral around a line of phase singularity. As such, it fits perfectly as an orbital angular momentum - it's no different than the angular momentum of an electron in a hydrogen atom. In a bucket, each particle has a different angular momentum but each particle still has orbital angular momentum. $\endgroup$ – Emilio Pisanty Apr 21 '17 at 15:50
  • $\begingroup$ @EmilioPisanty Yeah fair enough. I'm not "attached" to vorticity: I just remember this being treated separately from the other two in nuclear physics. Classically you are certainly right... $\endgroup$ – ZeroTheHero Apr 21 '17 at 15:53
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Not really. All angular momenta are either orbital, spin, or a linear combination of the two.

The worst you end up getting is wonky mixtures like these ones, where you mix the spin orbital angular momenta of different shells inside an atom in some weird order, or funky linear combinations of the two (and while we're at this, the photon spin has some tricky behaviour), but they all boil down to those two components.

More generally, there is a meaningful distinction between intrinsic angular momenta $\mathbf L_\mathrm{i}$, which do not change when you displace the origin, and extrinsic angular momenta $\mathbf L_\mathrm{e}$, which transform as $$ \mathbf L_\mathrm e\mapsto \mathbf L_\mathrm e'=\mathbf L_e-\mathbf r_0\times\mathbf P $$ when you displace the system as $\mathbf r\mapsto \mathbf r'=\mathbf r-\mathbf r_0$, and where $\mathbf P$ is the total angular momentum of the system. As regards your question, though, they are just descriptors that apply respectively to spin and orbital angular momenta.

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  • $\begingroup$ I felt a bit risky since the question I am asking is not something I can prove at my level. However, I trust what you say so here is the tick =) $\endgroup$ – SHY.John Apr 22 '17 at 7:41

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