Talk:Hydrogen atom

From Wikipedia, the free encyclopedia

WikiProject Physics This article is within the scope of WikiProject Physics, which collaborates on articles related to physics.
B This article has been rated as B-Class on the assessment scale.
High This article is on a subject of high importance within physics.

Help with this template This article has been rated but has no comments. If appropriate, please review the article and leave comments here to identify the strengths and weaknesses of the article and what work it will need.
Hydrogen atom was a good article nominee, but did not meet the good article criteria at the time. There are suggestions below for improving the article. Once these are addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.

Reviewed version: July 2, 2006

Contents

[edit] 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)

[edit] 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)

[edit] 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 (talk • contribs) 19:26, 19 December 2005

[edit] 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)

[edit] 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:
\psi_{nlm}(r,\theta,\phi) = \sqrt {{\left ( \frac{2}{n a_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:
L_\nu^\beta ( \rho ) = \sum_{m=0}^{\nu} (-1)^{m} \frac{(\nu + \beta)!}{m!(\nu - m)! (\beta + m)!} {\rho}^m \ ; \ \beta > -1
L_0^\beta ( \rho ) = 1
L_1^\beta ( \rho ) = - \rho + \beta +1
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)

[edit] 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)


[edit] 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)

[edit] 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

R(r) = \sqrt {{\left ( \frac{2}{n a_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 r to ρ, a factor dr / dρ is introduced in the integration. Hence,
\int r^{2} \left|R(\rho)\right|^{2} dr = \int r^{2} \left|R(\rho)\right|^{2} \frac{dr}{d\rho} d\rho
with
\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)