# How is angular momentum measured in experiments/in practice? [duplicate]

We read about and study angular momentum in quantum mechanics textbooks, its classical definition, its quantum definition, its mathematics, its representations, its eigenvalues and eigenfunctions...etc.

This is all lovely, but no books do not usually tell you how angular momentum is measured in experiments.

(Also, if someone knows a practical reference to quantum mechanics that would be awesome. Practical in the sense that, when mentioning that such an observable is described by a linear hermitian operator (which guarantees the reality of the eigenvalues, which are nothing but the spectrum we "find" in the lab) it would mention also how such a quantity is measured in practice in the lab)

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## marked as duplicate by Qmechanic♦, dmckee♦Jul 21 '12 at 15:04

Possible duplicates: physics.stackexchange.com/q/11197/2451 and links therein. –  Qmechanic Jul 21 '12 at 11:27
Books like Perkins describe many of the core methods of particle physics in the curse of introducing concepts in particle physics, and give the reader much of the foundation needed to follow the papers that experimenters write. –  dmckee Jul 21 '12 at 15:03
@Qmechanic: no. “11197” is explicitly about a fundamental particle. I already got a complain that my comment in “11197” is off-topical. –  Incnis Mrsi Aug 20 '14 at 11:04

For stable particles one can do a Stern-Gerlach experiment as mentioned by @user56771.

For elementary particles which decay fast, and resonances, one looks at the angular distributions of the decay products which will be different for different intrinsic spins of the parent particle. Once one builds a table for elementary particles the knowledge can be used with angular momentum conservation to limit the possibilities of spin,( as with the recent Higgs candidate, which can only be spin 0 or 2 because it decays into two photons,) even before there is enough statistics for definitive angular distributions.

Generally in particle physics one uses the angular distributions for spin questions. There is a talk on this on the CERN site.

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It isn’t correct to label all that stuff as elementary particles. These are subatomic particles. –  Incnis Mrsi Aug 18 '14 at 12:41

For the hydrogen atom, the way it is measured is by applying magnetic field gradients to electrically-neutral atoms. This will subject the atom to a force proportional to both the component of the magnetic dipole moment along the magnetic field and the gradient. The magnetic dipole moment itself is a function of the susceptibility $\mu$ and the total angular momentum, both angular and intrisic (spin). This is how the Stern-Gerlach experiment found out that there were particles of spin $\frac{1}{2}$

I'm not sure how you measure it on modern detectors as those used in ATLAS though.

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This answer is not very helpful because of unclear and confusing wording (namely, the use of demonstratives). One might expect that the Stern–Gerlach experiment determined the spin of silver atoms, but in fact it revealed only the angular momentum of the 5s electron (a trivial calculation shows that any silver atom of stable <sup>107</sup>Ag and <sup>109</sup>Ag isotopes can’t be a fermion); this thing is downplayed in most QM texts. The “answer” correctly reminds about “angular momentum”, but does not specify of which system. –  Incnis Mrsi Aug 19 '14 at 20:14
The experiment accounted mainly for electrons’ spin and the orbital angular momentum of nucleus–electrons system; nuclear magnetic momentum possibly is too weak. Of all 47 electrons only the 5s electron contributed since the remainder formed completely filled subshells. In short, there is no simple interpretation of this thing and the experiment, actually, didn’t clarify the question of spin of any particle. –  Incnis Mrsi Aug 19 '14 at 20:20