Talk:Good quantum number

"The hydrogen atom: no spin-orbit coupling"[edit]

The section "The hydrogen atom: no spin-orbit coupling" says

Thus, the good quantum numbers in this case, (which are the eigenvalues of these observables) are $l,j,m_{\text{l}},m_{s},m_{j}$ with a ref to Christman, Robert Eisberg, Robert Resnick, assisted by David O. Caldwell, J. Richard (1985). Quantum physics of atoms, molecules, solids, nuclei, and particles (2nd ed.). New York: Wiley. p. J-10. ISBN 047187373X.{{cite book}}: CS1 maint: multiple names: authors list (link)

However the ref actually says

would all be "good" quantum number but...

I think the ref could be read as "would all be swell quantum numbers however they are not ". Johnjbarton (talk) 02:04, 24 February 2024 (UTC)[reply]

The reference is trying to say that these all individually good quantum numbers, but one can't use all of them simultaneously. Here the next (unreferenced) section 'Complete set of commuting observables' also tries to explain the same thing. Jähmefyysikko (talk) 20:22, 26 February 2024 (UTC)[reply]

(This note was mainly to try to look for a less ambiguous ref). Johnjbarton (talk) 20:26, 26 February 2024 (UTC)[reply]

Weaker statement of conservation[edit]

At least as written here, the section "Weaker statement of conservation" is not directly related to the article.

The section reads like the topic is "conservation laws", part I and II. Good quantum numbers are only mentioned parenthetically in part I. I think the text should focus on the article topic.

(I also find these little math theorems to be annoying in physics articles. Not even a hint about what kinds of physical systems these issues bear upon.)

The next section "Analogy with classical mechanics" is interesting but flawed in two ways: without a reference that analogy appears to be WP:OR and the appearance of the Ehrenfest Theorem here and in case II (which does not explicitly discuss good quantum numbers) makes me wonder: how is this analogy related to the article topic? Johnjbarton (talk) 16:00, 26 February 2024 (UTC)[reply]

I don't think the 'weak conservation' is directly related to the topic, so I removed it.

With 'Analogy with classical mechanics', afaik there would only be a relation with the article topic if it discussed classical constants of motion. Good quantum numbers would the quantum analogues. Probably that's too much of a detour though. Jähmefyysikko (talk) 21:00, 26 February 2024 (UTC)[reply]

Removed the 'Ehrenfest' and 'classical' sections from the article per above. I also removed the 'proof' section, which was unsourced.

The remaining sections not very good yet. 'Conservation of good quantum numbers' and 'States which can be labelled by good quantum numbers' both discuss properties of states labeled with good q-numbers, and should be rewritten as a one section. Jähmefyysikko (talk) 05:27, 27 February 2024 (UTC)[reply]

To motivate this article, it might be a good idea to start by discussing constants of motion and how they allow a practical simplification in description of dynamics, and ultimately act as labels for the eigenstates. Then there is the discussion about symmetry: Some constants of motion can be identified via fundamental symmetries, and others are more subtle (like the Laplace-Runge-Lenz vector for hydrogen atom). Jähmefyysikko (talk) 08:51, 27 February 2024 (UTC)[reply]

collisions[edit]

The introduction has a paragraph on collisions which reflects the only meaning of "good quantum number" that I understood. Nothing in the article discusses collisions and thus we have no reference for this aspect. (I wonder if "good quantum number" has any practical use outside of collisions? The behavior of a system under a time-varying interaction naturally focuses on the varying parts, not the invariant part). Johnjbarton (talk) 16:07, 26 February 2024 (UTC)[reply]