# Talk:Hydrogen atom

## Density function image

I've made a newer version of the density function image, i think it should replace the old one.

Hydrogen

Yey or ney? —Preceding unsigned comment added by PoorLeno (talkcontribs) 22:52, 16 August 2008 (UTC)

## Relativistic effects of electron

The discussion of the speed of the electron stated that it "moved" at 1/100 the speed of light. My research shows that it's 1/10, and doesn't apply to the innermost shell. The primer I linked to includes the math. —DÅ‚ugosz

The speed of the electron is not a precisely definable quantity in a given energy state. However, the low-energy states have v/c on the order of the fine structure constant, which is closer in order of magnitude to 1/100 than 1/10.--76.81.164.27 05:59, 13 April 2007 (UTC)

## Deleted "Schrodinger's Paradox" Stuff

I'm a physics major at the University of Rochester, and came here to look up an equation for the ionization energy for the hydrogen atom for my statistical mechanics class. To my surprise, I found a section in the hydrogen atom article entitled "Schrodinger's Paradox". I deleted the section because it is utter pseudoscience and is misleading on a number of grounds. It's also original research, which has no business being on wiki. It was also biased towards the idea being correct. —Preceding unsigned comment added by 128.151.144.60 (talk) 01:55, 7 April 2008 (UTC)

User:200.222.237.108 has been going around adding fringe science junk to various articles. You just caught a chunk of it. Sorry. SBHarris 02:55, 7 April 2008 (UTC)

## Wave function

Although the wave function may be correct for a particular definition of the Generalized Laguerre polynomials, the expression in the article (before my edit) was not if we use the definition in the Laguerre polynomials. I think we should be coherent with the other articles, so I have changed the expression for the wave function to use those polynomials.

(I'm new at editing wikipedia, so if I haven't done anything properly, I would like you to tell me, please. Thank you). —Preceding unsigned comment added by John_C_PI (talkcontribs) 19:26, 19 December 2005

It seems to me that now the Laguerre polynomials in Wiki is consistent with the one with (n+l)! instead of (n+l)!3.But I want someone to confirm this before I edit the page.Send me a message if anyone agrees or disagrees with me.--Netheril96 (talk) 12:23, 10 September 2010 (UTC)

## GA on hold failed

Some minor things to adjust before the GA is awarded :

• Needs just a bit more references.
• The Mathematical summary of eigenstates of hydrogen atom section is really tough to understand by itself, it needs more text surrounding it. Lincher 15:48, 23 June 2006 (UTC)

Nothing was changed, the article will be failed. Lincher 13:44, 2 July 2006 (UTC)

## Wavefunction formula with (n+l)!^3

The wavefuction formulas on Hydrogen atom and Hydrogen-like atom were recently changed ([1] and [2], respectively) to have (n+l)!^3 instead of (n+l)!. I have come across several instances with the (n+l)^3 form (e.g. [3]); this also seems to contain the (n+l)!^3 version, but the generalized Laguerre polynomials have subscripts of n+l, instead of n-l-1 as they are in Wikipedia's articles. I am guessing that maybe separate definitions of generalized Laguerre polynomials are being used, as suggested by a comment above by User:John C PI (cf. this edit)? This page has the (n+l)! version (I am assuming the use of (n+1)! is a typo) with Laguerre subscript of n-l-1. I tried a quick check in my head for n = 2, l = 1; based on Eq. 33 and 36 at [4], it seems that the use of (n+l)! with the n-l-1 degree generalized Laguerre would give the (presumably) correct result provided here, whereas the n+l degree version would result in a polynomial in r of at least degree 3. (Also, the use of (n+l)!^3 instead of (n+l)! would seem to give a different constant muliplier than provided in the previous link.) I am going to revert the changes based on my limited investigation into this issue...if anyone is able to confirm the validity of my assessment or clarify the seemingly contradictory results that I found, that would be great.--GregRM 20:39, 29 January 2007 (UTC)

Yes, this is true. The problem is that different sources use different definitions for laguerre polynomials, and we expect Wikipedia to be consistent. In fact, when I studied the quantum physics subject (I'm a student of physics), it was very confusing that the two professors we had used different definitions! Anyway, the reversion you did is correct if we want to be consistent with the definitions in the Generalized Laguerre Polynomials article.
I don't remember which recognised books use which definition, and which is more widespread, since my references are my professor's notes, which are correct. But at the time I first dealt with this for some reason I thought the definition in the Generalized Laguerre polynomials article was more appropiate (at least, in this last article there is no history of doubt, and this is a good signal).
To clarify further doubts, this is a correct group of formulas and polynomials:
Wavefunction:
${\displaystyle \psi _{nlm}(r,\theta ,\phi )={\sqrt {{\left({\frac {2}{na_{0}}}\right)}^{3}{\frac {(n-l-1)!}{2n[(n+l)!]}}}}e^{-\rho /2}\rho ^{l}L_{n-l-1}^{2l+1}(\rho )\cdot Y_{l,m}(\theta ,\phi )}$
Polynomials:
${\displaystyle L_{\nu }^{\beta }(\rho )=\sum _{m=0}^{\nu }(-1)^{m}{\frac {(\nu +\beta )!}{m!(\nu -m)!(\beta +m)!}}{\rho }^{m}\ ;\ \beta >-1}$
${\displaystyle L_{0}^{\beta }(\rho )=1}$
${\displaystyle L_{1}^{\beta }(\rho )=-\rho +\beta +1}$
${\displaystyle L_{2}^{\beta }(\rho )={\frac {\rho ^{2}}{2}}-(\beta +2)\rho +{\frac {(\beta +2)(\beta +1)}{2}}}$
I hope this makes it a little more clear. John C PI 23:03, 29 January 2007 (UTC)
I just corrected this error (again) from another (well-intentioned) anonymous editor. We need to keep an eye on this one. —Preceding unsigned comment added by Stephenedie (talkcontribs) 02:22, 20 January 2010 (UTC)

I edited the subscript (degree) of the Laguerre polynomial appearing in the wave function and cited a couple of references that use this convention (n-l-1). I am happy to see the degree displayed as n+l, but please give a reference for this convention if you change it back. Cheers! — Preceding unsigned comment added by Micah.prange (talkcontribs) 15:26, 17 August 2011 (UTC)

The formula for the radial part is incorrect. If the generalized Laguerre polynomials are defined as in the corresponding article, than the correct factor should be (n+l)!, not [(n+l)!]^3. Just check the normalization condition. — Preceding unsigned comment added by 129.100.61.12 (talk) 17:05, 19 September 2011 (UTC)

A simple check in math program, e.g. Mathematica, confirms the correct normalization factor with (n+l)! in the denominator (not cubed). Here is the output:

In[1]:= ${\displaystyle R[n_{-},l_{-},r_{-}]:={\sqrt {{\left({\frac {2}{na0}}\right)}^{3}{\frac {(n-l-1)!}{2n((n+l)!)}}}}{\textrm {Exp}}[-{\frac {r}{na0}}]({\frac {2r}{na0}})^{l}{\textrm {LaguerreL}}[n-l-1,2l+1,{\frac {2r}{na0}}]}$

Spherical part

In[2]:= ${\displaystyle Y[n_{-},l_{-},\Theta _{-},\phi _{-}]:={\textrm {SphericalHarmonicY}}[n,l,\Theta ,\phi ]}$

Full wavefunction

In[3]:= ${\displaystyle \Psi [n_{-},l_{-},m_{-},r_{-},\Theta _{-},\phi _{-}]:=R[n,l,r]Y[l,m,\Theta ,\phi ]}$

Check normalization (3D volume integration in spherical coordinates, here for specific quantum numbers)

In[4]:= ${\displaystyle {\textrm {Simplify}}[\int _{0}^{\infty }(\int _{0}^{\pi }(\int _{0}^{2\pi }{\textrm {Conjugate}}[\Psi [n,l,m,r,\Theta ,\phi ]]\Psi [n,l,m,r,\Theta ,\phi ]r{\textrm {Sin}}[\Theta ]d\phi )rd\theta )dr}$
${\displaystyle /.\{n->2,l->1,m->1\},a0>0]}$
Out[4]= ${\displaystyle 1}$

Thomas.fernholz (talk) 14:52, 7 May 2012 (UTC)

In that case, I'm getting rid of the square brackets because I really thought someone removed the "^3" as vandalism, since the square brackets are completely redundant anyways. --Freiddie (talk) 23:54, 7 May 2012 (UTC)

The issue is that the article cites Griffith as the source of the equation but Griffith uses a different definition of the Laguerre polynomials, his are a factor of ${\displaystyle (n+l)!}$ larger. So people keep coming along seeing it's different from Griffith and adding the ^3 thinking it is a typo. I removed the reference to Griffith and added a note below pointing out this difference in definition. Now there is no reference for the equation, but none of the text books I have looked at use this definition of the Laguerre polynomials and give a statement of the general hydrogen wave function, even Messiah as far as I can tell. Timothyduignan (talk) 03:38, 4 December 2012 (UTC)

## poorly written

The level of this article is wildly inappropriate for the general reader. Much of the section "Features going beyond the Schrödinger solution" doesn't belong in this article. --76.81.164.27 05:56, 13 April 2007 (UTC)

Hear, hear! David F (talk) 03:19, 10 March 2013 (UTC)

## Atomic hydrogen

Atomic hydrogen and Hydrogen atom do NOT have overlapping meanings. This article is junk. Was it written by a non-native English speaker?71.31.145.210 (talk) 18:41, 16 March 2012 (UTC)

They can be used interchangeably (say, for isolated hydrogen atoms), or can have different meanings (as in compounds), thus I disagree. Materialscientist (talk) 00:32, 17 March 2012 (UTC)

## Eccess and Binding energy

"Eccess energy" and "binding energy" links to the same article, What is the diference? 80.24.186.207 22:42, 2 September 2007 (UTC)

The sign. 149.217.1.6 16:09, 27 October 2007 (UTC)
The explanation (the difference between an isotope's mass number and its actual mass in AMU (times c2, of course)) can be found at "Mass excess"; I have fixed the redirect. --DWIII (talk) 01:54, 28 September 2008 (UTC)

## Wavefunction and normalization

As a follow-up to the discussion above about the different definitions of the associated Laguerre polynomials, I have come across the following problem: The radial part of the wavefunction as given in the article

${\displaystyle R(r)={\sqrt {{\left({\frac {2}{na_{0}}}\right)}^{3}{\frac {(n-l-1)!}{2n[(n+l)!]}}}}e^{-\rho /2}\rho ^{l}L_{n-l-1}^{2l+1}(\rho )}$

doesn't (quite) seem to be correctly normalized. The integral over r2|R|2 yields the value 2 for n = 1, 1 for n = 2, 2/3 for n = 3, 0.5 for n = 4, etc. Could someone double-check this? 149.217.1.6 16:08, 27 October 2007 (UTC)

Follow-up: I found the source of the discrepancy. When making the change of radial variable from ${\displaystyle r}$ to ${\displaystyle \rho }$, a factor ${\displaystyle dr/d\rho }$ is introduced in the integration. Hence,
${\displaystyle \int r^{2}\left|R(\rho )\right|^{2}dr=\int r^{2}\left|R(\rho )\right|^{2}{\frac {dr}{d\rho }}d\rho }$
with
${\displaystyle {\frac {dr}{d\rho }}={\frac {na_{0}}{2}}}$.
With this additional factor, the integral over all space yields unity and the normalization condition holds. 149.217.1.6 20:18, 28 October 2007 (UTC)

## H-1

Is H-1 a proper notation for the hydrogen atom? The only article in which I've seen it used is Big Bang nucleosynthesis. It is also not mentioned in the disambiguation page H-1. Should it be added to this page? --George100 (talk) 13:05, 12 July 2008 (UTC)

You usually write either "1H" or "hydrogen-1". BTW, why does it say "This article primarily concerns hydrogen-1", and why does hydrogen-1 redirect here? I see absolutely no reason why the stuff in this article can't apply to deuterium or tritium. -- 10:29, 30 October 2008 (UTC)

## Incomplete and incorrect definition of j

I've chaged the definition of j: IIUC j is not an integer (it is an integer +/- 1/2). I've also added to the definition to clarify the meaning of 'total angular momentum'. I'm a bit rusty on this so please check! --Kevin Cowtan (talk) 12:11, 19 November 2008 (UTC)

## electron spin -- schrodinger equation / pauli equation /dirac equation

there seems to be a bit of a muddle here concerning the electron spin and the schrodinger equation. the normal unmodified schrodinger equation describes the behaviour of a spin zero particle, and as such will predict that a hydrogen atom is possessed of zero angular momentum in the ground state, contrary to what is observed. it is only when one steps up to the pauli a.k.a schrodinger-pauli equation that this defect is corrected. (or, of course, the fully relativistic dirac equation). this is not at all made clear in the present state of the article (march 2010), and will i fear need a deal of work to unravel. —Preceding unsigned comment added by 62.56.52.132 (talk) 22:51, 30 March 2010 (UTC)

## Wrong diameter for illustration

The diameter is given as 2.4 Angstroms, or "twice the Bohr radius." In reality the correct diameter is about 1.1 Angstroms-- about half this. I realize these things are not exact, but 1.1 A is much closer than 2.4 Angstroms. The original artist and uploader apparently is no longer active. I wonder if anybody would like to re-do this illustration? SBHarris 04:58, 19 May 2010 (UTC)

## Eigenstate 4,3,1, figure caption

There's a figure in the text showing a constant probability surface for the 4,3,1 state, the caption for which says, "The solid body contains 45% of the electron's probability." This is pretty ambiguous language, and it seems like it would be easy to misunderstand unless you already knew what it's supposed to mean; I mean, it contains "45% of the probability" for position measurements. I'm going to be bold and change it to say s/t like "3D illustration of the eigenstate ${\displaystyle \psi _{4,3,1}}$. Electrons in this state are 45% likely to be found within the solid body shown." I think this is a bit more precise, but it doesn't quite capture the fact that electrons aren't inside that space "45% of the time"; rather, position measurements are 45% likely to find them in that space. I haven't come up with a way to emphasize this subtle but key point in any kind of succinct way. I invite further suggestions for improved language. Flies 1 (talk) 16:27, 21 April 2012 (UTC)

## Apparent editorial comments moved here from the article

In this edit I removed the following text which had just been added by an anon to the Quantum theoretical analysis section of the article:

Emission spectrum of hydrogen. When excited, hydrogen gas gives off light in four distinct colours (spectral lines) in the visible spectrum, as well as a number of lines in the infra-red and ultra-violet. Bohr (and others) were aware of this and discovered orbitals happened to co-incide with wavelengths. From this exciting realization they began using electric force / motion functions and wave functions (Einstein) to explain the coincidence they saw in what they could only first imagine to be a classical orbit situation.

Before reading Schrödinger it's HIGHLY advised to check the acrticles concerning the spectrum of hydrogen and the articles concerning the simpler Bohr and Einstein models (which became quantum calculation) to see why these complexities became tried and relevant. (note also brownian motion and other experiments in the experiments listsing - these show allot too - and as well how often scientists move from bulk observation to particular causes and values underpinning)

Wtmitchell (talk) (earlier Boracay Bill) 05:25, 16 July 2012 (UTC)

## Dark matter

I removed the sentence about dark matter and dark energy from the lead paragraph because it was distracting. I left a link to the word "baryonic" in the preceding sentence, and that article mentions dark (non-baryonic) matter. If someone feels strongly about pointing out the difference between hydrogen and dark matter, I suggest it belongs somewhere other than the opening paragraph. -LesPaul75talk 18:08, 14 January 2014 (UTC)