Talk:Quantum number

Nearly-compatible quantum numbers

In the section "Spatial and angular momentum numbers" the article states "As per the following model, these nearly-compatible quantum numbers are [...]". What does nearly-compatible mean? I have not heard of compatibility of quantum numbers. If this is not a scientific term, I believe this should be clarified. If it is, including a citation or further explanation would be helpful. --abhandari (talk) 17:15, 7 January 2018 (UTC)

In the case of electrons, the quantum numbers can be defined as "the sets of numerical values which give acceptable solutions to the Schrödinger wave equation for the hydrogen atom"

The article says: In the case of electrons, the quantum numbers can be defined as "the sets of numerical values which give acceptable solutions to the Schrödinger wave equation for the hydrogen atom" Seems to me that this is true near some positive particle. Well, much of quantum numbers has to do with the quantum description of an atom, but all this is also more general. Quantum mechanics also describes, for example, the states of spin 3/2 negatively charged particles around a spin 2 positive particle. Seems to me that a good part of the article should describe the quantum mechanics of electrons around nuclei, that being a common situation, but not the only one. Gah4 (talk) 14:04, 10 September 2018 (UTC)

This is one of the silliest statements I've read on Wikipedia, and I'm surprised it's been around for so long. Wow. What does this even mean? I'm deleting it. Just wow. Ponor (talk) 17:22, 14 September 2020 (UTC)

dimensionality

It seems that the number of quantum numbers needed is related to the dimensionality of the system. It takes three quantum numbers for a hydrogen-like atom because we live in a 3D universe. Should this be mentioned here? Gah4 (talk) 18:40, 26 August 2019 (UTC)

I believe this is a misunderstanding. In addition to the degrees of freedom that arise from 3D space, particles can have internal degrees of freedom, like spin, and hence additional internal quantum numbers. — Preceding unsigned comment added by 2A00:23C7:9386:BA00:2C32:B9A0:1C47:6E99 (talk) 00:57, 19 June 2020 (UTC)

That is true, but I did say related. Note that quantum systems could be numbered with only one quantum number, but it would be more complicated. Instead of spin, one could use even/odd values after doubling some other quantum number. The whole set of quantum numbers is (usually) countably infinite. The quantum numbers that we use tend to correspond to classical quantities, and so have connection to system dimensionality. Gah4 (talk) 01:32, 19 June 2020 (UTC)

"The whole set of quantum numbers is (usually) countably infinite."

Yes, although the elements created to date stop at Oganesson, atomic number 2 + 4*(2^2 + 3^2 + 4^2) = 118. That fills up s,p,d,f and if anyone succeeds in pushing this to atomic number 121 (since 119 and 120 only need s again), f will need to be followed by g.

There has been some discussion of islands of stability, but the prospects for g followed by h any time this millennium seem pretty slim. Speaking as a pantheist who considers g*d to be the universe, I believe the universe doesn't want us to ever get even to g. Certainly not in my lifetime. Vaughan Pratt (talk) 00:13, 3 October 2023 (UTC)

Orbital hybridization

The rules subsection nicely uses carbon for an example. This might be a good place to mention that the basis for the numbering isn't unique, and, for examples, Sp3 hybridization. This is sort-of hinted at when it mentions linear independence earlier, but should be mentioned more. Gah4 (talk) 17:14, 1 May 2020 (UTC)

If we write the numbering system as (n, L, m, S) where n ranges from 1 to 7, 2L+1 ranges from 1 to n (so L ranges from 0 to 3), m ranges from -L to L, and S is either 0 or 1, then an equally good numbering system is (hn, T, L, m, S) where hn ranges from 0 to 3, T is 1 when hn == 0 and otherwise is 0 or 1, L ranges from 0 to hn, m ranges from -L to L, and S is either 0 or 1. Vaughan Pratt (talk) 00:37, 3 October 2023 (UTC)

Merger proposal

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.

To improve Quantum number rather than merge Good quantum number in. Klbrain (talk) 19:28, 27 December 2020 (UTC)

---

I propose to merge Good quantum number into Quantum number. There is no good reason that these should be two separate pages. I also note that what this article, in places, calls a quantum number, is more accurately called a good quantum number. Quantum numbers are more general; when they represent a conserved quantity they are referred to as good. Please also note that, although the Good quantum number article is shorter and less pretty than this one, it is far more accurate. I get the impression it was written by a professional physicist, whereas this article appears to have been edited by passionate amateurs (absolutely no offence meant by this). 2A00:23C7:9386:BA00:2C32:B9A0:1C47:6E99 (talk) 00:48, 19 June 2020 (UTC)

I think the Good quantum number page is fine, but it needs a new name. There is actually very little on actual quantum numbers. Otherwise, it seems that there could be (somewhere) discussion of allowed and forbidden transitions, which are related to quantum numbers, and especially that some are better than others. It seems that there is a page for forbidden transition but not for allowed transition. In any case, Good quantum number could be changed or renamed. Gah4 (talk) 01:26, 19 June 2020 (UTC)

I think you have misunderstood. It is this article Quantum numbers that is problematic. Some of the statements in it are simply false in general - instead they refer to particular cases of good quantum numbers. The whole article needs an overhaul. At the moment it is mainly describing good quantum numbers, not quantum numbers more broadly. A case could also be made for merging the articles with Complete set of commuting observables. I would strongly welcome the opinion of some professional quantum physicists 2A00:23C7:9386:BA00:FD4E:24FE:8C0D:1A4C (talk) 16:01, 19 June 2020 (UTC)

I suspect you could find something wrong with any article, but I do agree that this one could use some fixing. I am not sure that merging will fix it, though. I notice that Complete_set_of_commuting_observables#See_also seems to be a list of articles that might have too much overlap. (No pun intended. I didn't think of it until after I wrote it.) As above, though, I don't see so much wrong with Good quantum number except the name. There isn't much discussion of quantum numbers at all! Gah4 (talk) 20:44, 19 June 2020 (UTC)

Very good points, thanks. I'll give this all some more thought. In the meantime, other opinions are also welcome (that's of course the purpose of a discussion!) By the way, my motivation (speaking as a graduate student of quantum physics) is that so many maths/physics articles on Wikipedia are astoundingly good - i.e. better than a lot of textbooks. Unfortunately, the ones being discussed here just do not seem up to the same standard. Again, there's absolutely no disrespect or criticism intended, just a desire to help improve things as I love Wikipedia!2A00:23C7:9386:BA00:58DF:2ED1:A67A:6DFB (talk) 02:39, 20 June 2020 (UTC)

I think this page just needs a professional editor. Merging it with another page wouldn't do any good, as the mistake is intrinsic. Anyways, imma just put this topic into WT:WC just in case :). Good job fellow editors! Ice bear johny (talk) 15:15, 14 September 2020 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

What's the spin quantum number?

This article says $s$ is the "spin quantum number". The article spin quantum number starts by saying $m_{s}$ is the spin quantum number. But later at one point it calls $s$ the spin quantum number. $s$ and $m_{s}$ are different things, so this is a bit confusing.

Is there a standard definition of "spin quantum number", or do experts freely call both of these things the "spin quantum number"? If there's a standard definition, let's only call one of $m_{s}$ and $s$ the spin quantum number, not both. If there's not a standard definition, we should warn the reader. John Baez (talk) 19:52, 1 December 2021 (UTC)

I suspect people are lazy and use them wrong. Not only that, m_ℓ and ℓ also have that problem. When the distinction is needed, and often enough it isn't, both are used with distinct meanings. When the distinction isn't needed, it is convenient to use the ℓ and s. Especially since electrons are always spin 1/2, there is no need to remind people of that. Gah4 (talk) 21:04, 1 December 2021 (UTC)

There are two quantum numbers, $s$ for total spin and $m_{s}$ for projection of spin on $z$.

• Eisberg, Robert, and Robert Resnick. Quantum physics of atoms, molecules, solids, nuclei, and particles. 1985. Page 274.

Johnjbarton (talk) 03:46, 16 February 2024 (UTC)

Misuse of "integer" and "half-integer".

This article mixes up energy levels with transition energies and implies that measurements arrive at integer values. EG "quantities can only be measured in discrete (often integer) values." Johnjbarton (talk) 19:00, 5 February 2024 (UTC)

Symmetry

Discussion about the relation between symmetry and some of the quantum numbers, like those related to angular momentum, should be added. I don't have a reference in mind, but most of the advanced QM textbooks probably discuss such things. Jähmefyysikko (talk) 07:07, 22 February 2024 (UTC)

You might take a look at

• Greiner, W.; Müller, B. (1994). Quantum Mechanics: Symmetries (2nd ed.). Springer. p. 279. ISBN 978-3540580805.

from Springer. Johnjbarton (talk) 23:42, 29 February 2024 (UTC)

Need a section History and on Hund's rules and Pauli

The current article starts with "Mathematical origin", implying that quantum numbers are a math thing rather than the other way around. The origin story for quantum numbers is vital to even understand why they are notable.

Central to the understanding of quantum numbers is Pauli's symmetry principle: without it we only need one quantum number ;-)

Hund's rules also deserve a section as they summarize the way that the electron quantum numbers (occupying most of the current article) impact chemistry. Johnjbarton (talk) 16:36, 22 February 2024 (UTC)

Another problem with the article is the definition which assumes quantum numbers are conserved, making this duplicate of good quantum number. And even if the assumption of conservation is relaxed, the overlap remain quite significant. (Complete set of commuting observables is not too far either, but has more mathematical emphasis). Jähmefyysikko (talk) 20:25, 23 February 2024 (UTC)

Conceptually these might overlap, but the content of the articles seem independent. This page does not even discuss conservation after the first sentence and the short description. Maybe we can have a summary section linking good quantum number? Including your suggestion about symmetry? Should connect with Yang-Mills theory and Spin–statistics theorem?

To be honest I'm not clear on how this overall topic should be handled. The electron section is good, provides a nice concrete example. But I don't think the article gets across the various meanings of quantum number, most especially its meaning as "a quantized degree of freedom for a particle". A symmetry/conservation section could help. Reworking the section "mathematical origin" might help.

I'll look in to a History section, summary mainly, so much appears in other articles. Johnjbarton (talk) 00:29, 24 February 2024 (UTC)

The conservation is assumed in the 'Mathematical origin' section when the operators are required to commute with the Hamiltonian. It is implicit in later sections also: for spin-orbit coupled systems it leads us to reject the orbital/spin angular momentum basis; for elementary particles there is some related discussion about symmetries. My guess would be that it is easiest to approach the concept by starting with good numbers, and only later mention that even if the symmetries are broken, the same numbers can be used to describe the system.

For Yang-Mills and Spin-statistics, I don't immediately see the connection. Making a connection to a 'degree of freedom' is a good idea. Jähmefyysikko (talk) 13:20, 24 February 2024 (UTC)

I added a small section on this, mainly to link the topics and "Aufbau principle" and Hund's rules. Johnjbarton (talk) 00:05, 24 February 2024 (UTC)

I added a History through 1953. I tried to avoid being expansive and just focus on "quantum number".

I set it at the top as is common but the bottom is also common and fine by me. I would actually prefer the top to have a good short section on 'definition' but the math one.

@ReyHahn please check. Johnjbarton (talk) 19:08, 26 February 2024 (UTC)

Looks good. Much better than the rest of the article at the moment. The definition should indeed go to the top, unless the introduction is extensive enought to make it redundant. Jähmefyysikko (talk) 20:09, 26 February 2024 (UTC)

Different meanings of quantum number.

I think on of the issues here is that different sources from different fields use the term. Atomic physics uses "quantum number" in two ways: as a quantized degree of freedom ("orbital angular momentum quantum number") and as an identifier for an energy level ("l=1 for p orbitals"). Particle physics uses the first meaning mostly. Ref:

• Quantum physics of atoms, molecules, solids, nuclei, and particles by Eisberg, Robert Martin; Resnick, Robert.
  • Page 20: $nh\nu$, the $n$ is a "quantum number". So an integer scalar I guess.
  • Page 100: values in Bohr's radii formula. So a integer marker identifying a state.
  • Page 238: values in Schroedinger atom formula. Again an identifier.

VS:

• Griffiths, David. Introduction to Elementary Particles. Germany, Wiley, 2020.
  • "The answer is that neutrons carry other 'quantum numbers' besides charge (in particular, baryon number), which change sign for the antiparticle." So a quantized degree of freedom.

Johnjbarton (talk) 01:05, 24 February 2024 (UTC)

I don't see that there would be two really distinct meanings here. It is just that in the first case the quantum number l is not specified, and in the second one it is set to l=1. I tried to check what Eisberg and Resnick write on those pages, but this must be different edition and the pages don't quite match (and I'm not sure how different the text would be from your edition).

I understand the set of quantum numbers as essentially the eigenvalues of a commuting set of observables (or closely related to them, as with $L^{2}$ operator and $l$) that we use to label the quantum states. This is how Bruus and Flensberg use the term:

In general a complete set of quantum numbers is denoted $\nu$ . The three examples given above corresponds to $\nu =(k_{x},k_{y},k_{z},\sigma )$, $\nu =(n,l,m,\sigma )$, and $\nu =(n,k_{y},k_{z},\sigma )$ each yielding a state function of the form $\psi _{\nu }(r)=\langle r|\nu \rangle$. The completeness of a basis state as well as the normalization of the state vectors play a central role in quantum theory

The examples are the free particle, hydrogenic atom and a free electron in a magnetic field in Landau gauge. Here the quantum numbers are not necessarily discrete, as momenta are also referred to as quantum numbers.

The symmetry discussion actually seem to belong more to the good quantum number article (I wasn't aware of that previously). Jähmefyysikko (talk) 09:23, 24 February 2024 (UTC)

Sorry I should have given the link to Eisberg/Resnick book. I was using the 1985 edition and didn't realize the 1974 edition was also online.

Ok, maybe I am making too much of the difference between a quantum number and its value. Particle physicists tend to focus on the "set of quantum numbers", per your quote above. Chemist and atomic physicists get very personable with the values, eg "ℓ = 0 is called s orbital, ℓ = 1, p orbital, ℓ = 2, d orbital, and ℓ = 3, f orbital." Q: "What's the quantum number for a d orbital?" Chemist: "Oh it's 2." Physicist: "Huh? It is orbital angular momentum, l, with value 2".

I just suggest that this may account for some of the lack of clarity in the article. Johnjbarton (talk) 16:14, 24 February 2024 (UTC)

Here is a quote that gets at the issue I was trying to suggest:

• "In other words, the quantum numbers satisfying the principle of per- manence, n and k, could serve as labels of the various electronic groups and subgroups."

The "permanence" of quantum number values seems unremarkable to us, but the labeling of atomic levels by a few words vs a value from a continuum revolutionized chemistry.

The context here is Pauli's exclusion principle work and the periodic table; (k will be renamed l, azimuthal, later).

• Darrigol, Olivier. "8. A Crisis". From c-Numbers to q-Numbers: The Classical Analogy in the History of Quantum Theory, Berkeley: University of California Press, 1992, pp. 175-212. (In De Gruyter library)

This source is quite detailed so I'm unsure how useful it will be. And I'm now convinced not to make an issue of the "identifier" aspect. Johnjbarton (talk) 18:17, 24 February 2024 (UTC)

Template:Flavour_quantum_numbers

Template:Flavour_quantum_numbers links this article with text "flavour quantum numbers". Sadly this page has almost nothing to say about that topic. Johnjbarton (talk) 23:16, 29 February 2024 (UTC)