Talk:Helium atom

We need some explanation
The technical math of this page is unavoidable, but some things are abbreviated (like "a.u.") which need to be written out at least once. As it is, I can't even tell which notation is being used for first and second ionization energies (though I know the first one is about -26 eV), and if the ground state (negative) binding energy is the sum of these two ionization energies, or what. If these can be fully written out, this article could be a nice resource, and would deserve to be mentioned as a main article in the Helium article, perhaps for a "Quantum mechanics of the helium atom" subsection. As it is, I can't understand enough of this article to summarize it. Can you creators help? It would also be nice if you'd all assign yourself usernames and talk pages, too. It helps a lot with discussions and colaboration. S B Harris 01:58, 12 June 2009 (UTC)

What the heck is going on in #Thomas–Fermi method?
You write the general idea of the TF method, then you write $$ \int \frac{e^2 \rho(\vec{r'})} {|\vec{r} - \vec{r'}|} d^3r' = \frac{e^2}{4\pi\epsilon_0} \frac{1}{|\vec{r}_1 - \vec{r}_2|}$$ without explaining why, and get back to the original Hamiltonian, to solve it with the variational method. Why? -- A. di M. – 2009 Great Wikipedia Dramaout 14:43, 18 July 2009 (UTC)

Where are spins?
Ortho- and para- ? --93.73.27.16 (talk) 16:55, 28 January 2010 (UTC)

Not up to date
This site is important but not up to date. It does not mention the very precise calculations by G.W.F. Drake, John Morgan III,  Jon Baker, and Robert Hill on the Helium atom eigenstates. There is a whole literature and body of work which is not even being mentioned.

I'm missing the recent work of K. Pachucki who has done much on improving the QED contributions to the calculations of helium. Some of the work of his group on helium (in order): PHYSICAL REVIEW A 74, 022512 (2006); PHYSICAL REVIEW A 74, 062510 (2006); PHYSICAL REVIEW A 76, 059906E (2007); PHYSICAL REVIEW A 79, 062516 (2009); PHYSICAL REVIEW A 80, 019902E (2009); PRL 104, 070403 (2010); PHYSICAL REVIEW A 85, 042517 (2012); I think I'm not the one to dig into this though (unfortunately) Another question is if QED should be treated on this page, however, it's comment line says that it's on the physics of helium, so it sounds in place to add three body QED corrections here as well?

76.126.216.229 (talk) 00:10, 18 October 2010 (UTC)
 * Okay. WP:SOFIXIT. It's your encyclopedia, too. S  B Harris 05:02, 18 October 2010 (UTC)
 * I will take that as a green light and go ahead.  —Preceding unsigned comment added by 12.169.97.130 (talk) 17:46, 18 October 2010 (UTC)
 * Hello again. Just did it.  —Preceding unsigned comment added by 12.169.97.130 (talk) 18:06, 19 October 2010 (UTC)

Shouldn't the contributions of Nakashima and Nakatsushi (2007) be considered as well? I found this article and I thought it could be appropriate. 217.200.201.117 (talk) 17:07, 18 May 2015 (UTC)

Experimental value
The values of first and second ionization energies seem to be exchanged.Grausvictor (talk) 14:23, 29 April 2016 (UTC)
 * You were right. I have rearranged this section. Graeme Bartlett (talk) 01:24, 30 April 2016 (UTC)

Simple Formula -49/17(1-alpha)
Toward the end of the page, there's a quick note to say that the most accurate way is to use the formula energy (hartree) = -49/17(1-alpha).

What is this? Is it just a noted coincidence, or is it theoretically derived? H123b wiki (talk) 07:45, 7 February 2018 (UTC)
 * Thanks for complaining, It was vandalism by 116.199.64.68. I have removed it. Graeme Bartlett (talk) 10:34, 7 February 2018 (UTC)

I had an IP search for that IP: seems to be a chinese IP, and I suspect that it was probably well-meaning, but yeah, misunderstood the sense in which an equation is useful. On the other hand, the approximation is strikingly good: It seemed to be accurate to one part in hundreds of millions (unless my maths was wrong), which is quite good considering the search space for similar equations is probably only millions: a 1-in-100 coincidence, I reckon. — Preceding unsigned comment added by H123b wiki (talk • contribs) 22:00, 7 February 2018 (UTC)
 * I did a google scholar search, and came up with nothing, so perhaps it was not vandalism, but may be original research in good faith. It never had a source given. Graeme Bartlett (talk) 08:51, 8 February 2018 (UTC)

Questions about the section on The variational method:

Assuming the undefined quantity a (which I am guessing is the Bohr radius, usually denoted a_0; it should be defined) is a constant, the initial wave function given does not seem to have any parameters to be varied, so it seems rather confusing to say that this is an example of the variational principle. Only when one later adds the variational parameter Z does it seem that one is using a variational principle.Donpage (talk) 22:53, 3 January 2022 (UTC)