Talk:Azimuthal quantum number

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I've replaced the term state with the more appropriate orbital, as state refers to the combined condition of all the electrons in the atom, rather than the one (or two) in the orbital.--Ian 08:21, 30 Jan 2005 (UTC)

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Notation ℓ vs. $l$

I'm wondering what is the standard notation for the azimuthal quantum number. The article uses the handwritten letter-like “ℓ” (\ell), but outside of Wikipedia in textbooks and papers I see the normal “l” ($l$) pretty much everywhere. Is there a special reason why this article deviates from the standard notation? Is there a very important source that suggests the special letter “ℓ”? I checked a couple of books, and the following use “$l$”: Lectures on physics (Feynman), Introduction to Quantum Mechanics (Griffiths), Modern Quantum Mechanics (Sakurai), Course of Theoretical Physics (Landau-Lifschitz), Molecular Quantum Mechanics (Atkins), Atomic Physics (C. Foot), Quantenmechanik (Schwabl), Quantum Physics (Gasiorowicz), Quantum Physics (Le Bellac), Quantum Physics (Newton), Principles of Quantum Mechanics: as Applied to Chemistry and Chemical Physics (Fitts), Introduction To Quantum Theory And Atomic Structure (Cox)..., and many many more.
On the other hand I've only seen one book using “ℓ”, namely Quantum Physics (Scheck). Also, Handbook of Atomic, Molecular, and Optical Physics (Drake) switches between “$l$” and “ℓ” in different chapters.
If Wikipedia establishes a non-standard notation, there will be two different ones floating around for a long time. --Geek3 (talk) 20:53, 26 March 2018 (UTC)

I agree that there is no reason to use a special "l".

Also, The passage

While many introductory textbooks on quantum mechanics will refer to L by itself, L has no real meaning except in its use as the angular momentum operator. When referring to angular momentum, it is better to simply use the quantum number ℓ.

is personal opinion and goes against the NPOV rule. The most common convention in atomic physics is to use L when there is more than one electron.

Cdion (talk) 09:13, 10 December 2018 (UTC)

Proposal to rename to "Orbital quantum number"

As far as I can tell, "azimuthal" is Sommerfeld's original name for the quantum number later identified with electron orbital angular momentum. All of the books and papers I have read use the term "orbital", not "azimuthal". Eg Text books by Schiff, by Levine, by Karplus and Porter, by Eisberg and Resnick. The only place I found azimutal was in Whittaker's history book. Johnjbarton (talk) 23:21, 19 February 2024 (UTC)

• Oppose There are two quantum numbers for angular momentum: l the quantum number for total angular momentum and m for the z component (or other component in arbitrary direction). Xxanthippe (talk) 00:20, 20 February 2024 (UTC).

  @Xxanthippe I believe you are thinking about (intrinsic) nuclear spin angular momentum, which we don't seem to have a good page for. Maybe Nucleon_magnetic_moment?

  In the case of the electron in an atom we have four angular momentum quantum numbers s, m_s, l, m_l, or in jj coupling, two j and m_j. This "azimuthal" article is about l and m_l, but it's an older term, most textbooks use "orbital angular momentum".

  Would you reconsider? Johnjbarton (talk) 00:43, 20 February 2024 (UTC)

• Oppose, lets not change unless needed, both are used. I would change the first sentence to "the azimuthal quantum number or orbital quantum number". I think this is better than shoving that term to the end of the paragraph. Ldm1954 (talk) 00:51, 20 February 2024 (UTC)

  Can you add a reference for this name? That's where I started, I couldn't find one. Johnjbarton (talk) 00:55, 20 February 2024 (UTC)

  The literature is all over the place, for instance Google searches on "orbital quantum number" and "azimuthal quantum number" both give many hits. One of the reasons is that the main current uses are:

  a) Undergrad texts

  b) Ab-initio, where pure states are rarely present, but one often projects the spherical harmonics of orbitals centered on atoms onto hydrogen-like states to model spectra or similar.

  I have doubts that there is enough in a name, particularly as except for describing spectra the terms are dodgy at higher ab-initio levels. Ldm1954 (talk) 01:09, 20 February 2024 (UTC)

• Oppose. I don't see that 'orbital quantum number' would be more common than the self-explanatory 'orbital angular momentum quantum number' or the traditional 'azimuthal quantum number'. Of the works mentioned above, Karplus & Porter (1970) introduce it as azimuthal quantum number, Schiff (1968) as orbital-angular-momentum quantum number. Jähmefyysikko (talk) 08:54, 20 February 2024 (UTC)

  I guess the tradition is "azimuthal" for chemists and "orbital" for physicists ?

  So far we have one source and many memories ;-) Johnjbarton (talk) 17:22, 20 February 2024 (UTC)

  Griffiths (3rd ed.) also introduces it as azimuthal, but says the traditional names for the quantum numbers are "unfortunate". Later he uses orbital angular momentum quantum number as the name. Landau & Lifshitz (non-relativistic QM) says it is "sometimes called azimuthal", with no alternative name given. The ISO standard 80000-10:2019 uses "orbital angular momentum quantum number". Jähmefyysikko (talk) 18:03, 20 February 2024 (UTC)

  Thanks! I'll make some Nomenclature paragraph. Johnjbarton (talk) 18:24, 20 February 2024 (UTC)

• Weak oppose I learned about this number with this name (azimuthal), I would try to figure out from which textbook.--ReyHahn (talk) 09:16, 20 February 2024 (UTC)
• Strong oppose as needlessly confusing. Although according to others here "Orbital quantum number" is used for this topic, an atomic orbital has three quantum numbers. The proposed title would mean the article would have to start by a this-not-that definition to disambiguate this topic from principal quantum number and magnetic quantum number. Compare to how atomic orbital#Complex orbitals lays out the different quantum numbers of an orbital using distinct names. DMacks (talk) 09:25, 20 February 2024 (UTC)

  I'm confused. How would "orbital quantum number" be any more ambiguous than "azimuthal quantum number"? Both are exactly as distinct. (The atomic orbital link you posted is one of the very few places in Wikipedia that seem to use "azimuthal" other than this article. The quantum number for the angular momentum of the orbital is called "orbital angular momentum", whereas "azimuthal angular momentum" is not thing; logically the corresponding quantum number is... called something historical.) Johnjbarton (talk) 17:21, 20 February 2024 (UTC)

  They are all quantum numbers that identify a specific atomic orbital, therefore in lay language they are orbital quantum numbers. DMacks (talk) 20:17, 20 February 2024 (UTC)

• There is confusion here about association with atomic electrons. The nomenclature applies to all angular momentum. See Angular Momentum book by Edmonds.Xxanthippe (talk) 21:46, 20 February 2024 (UTC).

  Do you mean:

  • Angular Momentum in Quantum Mechanics By A. R. Edmonds · 1996

  I didn't find anything about "azimuthal" via Google books or the online pdf preprint images at CERN Johnjbarton (talk) 22:51, 20 February 2024 (UTC)

  In principle I agree with Xxanthippe. This is a good quantum number in any system with full rotational symmetry and no spin-orbit coupling. On the other hand, of such systems hydrogenic atom is by far the most important, so the emphasis on it is not unreasonable. But if there are sources, some general discussion could be added (e.g. examples of other systems and about the required symmetries). Jähmefyysikko (talk) 10:09, 22 February 2024 (UTC)