Talk:Particle in a spherically symmetric potential

message: Hi. The equation after "This gives an equation in which all natural constants are hidden," seems to be missing a first derivative that you get from the product rule. It seems incompatible with this one. Any thoughts?
Tinos (talk) 08:07, 12 May 2010 (UTC)
thread_title:  Possible Error in Hydrogenic Section 

message: What went before:
:After some discussion HappyCamper and I derived a normalization constant that differed from the one in Mathews, P.M.; K. Venkatesan (1978). A textbook of quantum mechanics. McGraw Hill.. See the version of the article  of  02:57, 2 June 2007 and talk under heading "Extra factor". --P.wormer 08:21, 2 June 2007 (UTC)
replies: text: Here is the link. --HappyCamper 17:31, 2 June 2007 (UTC)

text: I agree more or less with your thinking. Too many derivation details at the moment, and it detracts from the essentials. I'm tempted to move this derivation to a new page say quantum isotropic oscillator where we could potentially expand on D-dimensional isotropic oscillators, and also make some correspondences between the 2D system and the Morse oscillator. Then, on this page, we can just put the essentials: Radial equation, normalized wavefunction, general properties of the states, et cetera. I like the double factorial, simply because it's easier to remember. As for the equation hiding, if we move the material to a new article, then it may not be essential. It's probably easier to do this, but I would like to experiment with the HTML/CSS here as well. Which math article has these? I have some things to do outside of the Wiki as well. I'll wait for you to double check your notes. In the meantime, I'm going to see if I can find another textbook that has this constant written out. --HappyCamper 17:31, 2 June 2007 (UTC)
replies: text:  I tried very hard to find an article with the [hide] macro, but could not find it anymore. I remember that I looked at it and that it was based on the css visibility: hidden attribute. Anyway, I would prefer to have extensive derivations hidden by default and to have a show macro to pop them up. For the time being we may give the final result (normalized radial wavefunction) first and then give the derivation. --P.wormer 09:41, 11 June 2007 (UTC)

text: With regard to moving contents: the 3D oscillator fits very nicely in the present article because it starts from the equation for u(r) that was derived for all central symmetric potentials. The 2D oscillator is almost the same (also Laguerre for the radial part). It could go in here. I don't know about higher than 3D (except, of course,  Cartesian plus 2nd quantization), although I could imagine that hyperspherical harmonics could be useful for 4D.--P.wormer 09:41, 11 June 2007 (UTC)

text:  I performed the restructuring (separation of result from derivation). I used "my" form of the normalization constant in presenting the result, because I feel that neither the Gamma function nor the double factorial are widely known (especially not among chemists).--P.wormer 12:35, 11 June 2007 (UTC)
replies: text: I couldn't find anything useful either. But I'm sure I've seen them somewhere too. Anyway, I resorted to asking on the help desk: . Hopefully we will get a useful response. The higher-than-3d will be for another day. Thanks for the restructuring - the normalization constant looks great! --HappyCamper 02:46, 12 June 2007 (UTC)
thread_title:  Normalization 3D harmonic oscillator functions. 

message: Who put the cleanup template in the article and why?--P.wormer 12:41, 11 June 2007 (UTC)
replies: text: Looks like the cleanup tag was placed in December 2005...someone probably noticed that the image links were dead. The images were deleted almost a year earlier on January 2005. . I'm not sure how it ended up being at the top. I think we can remove it though. A nice thing to do for this article is to add pictures, but I don't think I will get to that anytime soon. --HappyCamper 02:32, 12 June 2007 (UTC)
thread_title:  Cleanup template 

message: Peter Atkins's popular (but comparatively deep) science book, Galileo's Finger: The Ten Great Ideas of Science (2003) mentions the coulomb potential energy as having 4D symmetry, which he says is responsible for the degeneracy (or near degeneracy?) of e.g. 2s and 2p orbitals in hydrogenic atoms, but not for those with more than one electron; indeed, he provides a beautiful and convincing illustration of how a spherical s-orbital can be rotated into a two-lobed p-orbital!). But nowhere does he seem to clarify what the 4th component of the symmetry is [e.g. I don't see how it could be a symmetry in time as well as space]. I've searched the web on "coulomb 4D symmetry" etc., but found nothing that seems to clarify the basis for the 4D symmetry. (The closest ref might be the J D Jackson reference at the end of the main Gauge Fixing page, but it doesn't mention 4D symmetry.) Would the "Particle in a spherically symmetrical potential" page be a suitable place to open up this aspect in a little more depth for enquirers at my level (PhD in chemistry but my maths and group theory are not at the level of a graduate physicist). If this is not the best place in the wikipedia, perhaps someone could kindly point me to a more apt location to ask. Thanks. 163.119.193.40 20:37, 14 August 2007 (UTC)
replies: text: Hmm...try at the Mathematics reference desk. They often like to try and answer these sorts of interesting questions. Hope this helps, and do check back frequently here as well, since others might have other ideas for you to pursue as well. (Wikipedians generally don't answer queries via e-mail, so I removed it from your post.) HTH. --HappyCamper 03:32, 15 August 2007 (UTC)
replies: text: Thanks. And I wasn't expecting an answer via email - I just couldn't see how to put an equivalent of your "Happy Camper" in, so I signed it with my email address. 163.119.193.40 11:46, 15 August 2007 (UTC)
replies: text: No problem. Since you're editing anonymously, Wikipedia uses the string of 4 numbers as your signature in place of a username. --HappyCamper 16:07, 15 August 2007 (UTC)
thread_title:  Query re 4D symmetry of coulomb potential energy 

message: Disclaimer:  I understand this is not the Intended use of editing talk in Wikipedia, still I Want to give this Avenue a shot, you understand. I'm a person who found quartz in a piece of family property in NY. I am not a Chemist or Quantum scientist of any sort, that being said I am competent enough to figure it out if I can attain some sort of relevent context with which to begin.
I want to understand holistically and in scientific terms the phenomenon of luminescence and sometimes phosphorescence specific to an estimated 65% of Herkimer Diamond Quartz Crystals reacting to shortwave UV exposure* Specifically I'm searching haystack upon haystack for the allusive - semi-Layman's termed - "needle" I can use to at least narrow my search to hydrogen like atomic structure, spherical harmonics, some sort of inclusion (iron and Hydrocarbon are common but visible without the use of UV radiation) please help me navigate the everchanching absolutes of science for my goal of.. personal entertainment.
*I'm a hobbyist of circumstance and do not offer this study to science as a valid or relevant statistic — Preceding unsigned comment added by HerkimerDiamondMineralMama (talk • contribs) 07:43, 28 March 2020 (UTC)
thread_title:  ??? 

message: Is the [(n+l)!]^3 factor in the normalisation of the hydrogen-like solution correct? Should it not just be (n+l)!, as on the main page on the subject? Anon1759 (talk) 17:40, 8 November 2020 (UTC)
thread_title:  Normalisation of Hydrogen Solution 

message: The introduction may be less jargonry, but is definitely more errorly. Eigenvalues are real numbers and not (wave)functions. --P.wormer (talk) 06:56, 11 December 2022 (UTC)
thread_title:  Make the introduction less jargony