Talk:Avoided crossing

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It is stated that triatomic molecules can only cross at a point. I don't think this is correct: 3*3-8 = 1 so surfaces can cross along a one-dimensional manifold, e.g. a line.

Why 3*3-8 = 1 (why minus eight)? Anyway, I think that depends on the molecule being linear or not. 
This article is very unclear by the way. There isn't even a definition of what an avoided crossing is.  —Preceding unsigned comment added by 178.199.32.49 (talk) 18:29, 6 January 2011 (UTC)

→I think this post is quite irrelevant now.In.santanu (talk) 22:36, 19 October 2013 (UTC)

There is not much correct in this article:

• The sentence

"The eigenvalues of a Hermitian matrix depending on N continuous real parameters cannot cross except at a manifold of N-2 dimensions. In the case of a diatomic molecule (one parameter, which describes the bond length), this means that the eigenvalues do not cross." is wrong (take the diagonal 2x2 matrix Diag(1,A) with eigenvalues one and A, where A is our real parameter. When changing A from zero to two we see a crossing in contradiction to the sentence (N=1).

• Also "In the case of a triatomic molecule, this means that the eigenvalues can intersect at a point only (see conical intersection)." is at least missleading - in 3 dimensions conical intersections are not points but lines (one dimensional).

Hope someone takes the time to improve it soon. Ciao. --Falktan (talk) 13:53, 25 June 2013 (UTC)

→Your example of diagonal matrix would not result into any avoided level crossing by it's very construction. You have choosen off-diagonal terms to be zero and have asymmetric elements. Hence for N=1 parameter you can have crossing in N-1=0 dimensional manifold, i.e a point.--In.santanu (talk) 16:23, 6 November 2013 (UTC)

→Conics may intersect on a point. One example would be two cones meeting on their vertices.In.santanu (talk) 22:32, 19 October 2013 (UTC)

I think your concern is met. --In.santanu (talk) 16:30, 6 November 2013 (UTC)

Erstwhile

Hi everyone. This is probably an unnecessary concern but 'erstwhile' might be an unfamiliar word for a general audience. I am a native English speaker and I work in the field of quantum chemistry / quantum information - so I feel that if I found this word unusual, others might also. Not to say 'erstwhile' is improperly used - I just want to make sure that the language is accessible. 172.91.74.198 (talk) 19:30, 28 June 2025 (UTC)

Done. Please consider next time editing it yourself. --ReyHahn (talk) 09:49, 29 June 2025 (UTC)