Talk:WKB approximation

message: The link to one loop diagrams should be explained. It isn't clear to me at all. The WKB approximation typically yields nonperturbative results. Take e.g. the hydrogen atom in an electrical field. The tunneling rate to the ionized state is proportional to Exp[-constant/|eE|], which is nonperturbative in the coupling (the charge e). To obtain this result from perturbation theory you must perform a resummaton over an infinite number of terms. So, perhaps by 'one loop effect' a summation over all one loop diagram is meant?Count Iblis 22:35, 2 September 2005 (UTC)
thread_title:  One loop diagram 

message: The demonstration given is not conclusive at all.
"The demonstration given is not conclusive at all."
If by that you mean that the derivation is incomplete, then I concur.--Paul 03:22, 26 October 2005 (UTC)
thread_title:  Demonstration 

message: I'd like to refer to an equation here from another article.    The reference would be simpler if there were equation numbers, but perhaps we aren't doing equation numbers in WP?   Alison Chaiken 18:35, 21 January 2006 (UTC)
replies: text: Equation numbers and references/citations have to be put in by hand. In case of references you can use the pair of commands    and a matching   command, but this doesn't work if you want to refer to a Ref. twice. Perhaps we need to talk to some of the administrators here, because making small edits to articles with a lot of numbered references like this one can be time consuming.Count Iblis 23:23, 21 January 2006 (UTC)
replies: text: What I ended up doing was putting in this: .    Maybe that's not exactly the right thing to do but it's the best I could figure out from Help:Anchors.    I don't quite know what you mean by "  and a matching  " since the only help pages I find that use "" are about templates.    As far as I can tell, there's no way to search within the "WP:Help" subspace.   Alison Chaiken 01:17, 22 January 2006 (UTC)
replies: text: I used the  in the article digital physics. You get automatically numbered references that act as links to the citations, but it doesn't work if you refer to the same citation more than once. I didn't previously know about the Anchor command you have used, though!Count Iblis 13:52, 22 January 2006 (UTC)
thread_title: Equation numbers?

message: Shouldn't this article include a mention of the cases where the WKB approximation gives the exact solution?  I don't remember them all off hand, but maybe I'll add them later. Or some else can doesn't matter to me. 
24.59.193.0 04:01, 8 March 2006 (UTC)
thread_title:  Missing Info 

message: Psi=exp(phi) and Psi'=A+iB, but then the following statement below is not true, cause the DERIVATIVE of Psi equals A+iB and not Psi directly:
The amplitude of the wavefunction is then exp[A(x)] while the phase is B(x).
Better remove it completely?62.218.164.30 17:54, 17 November 2006 (UTC)
thread_title:  wrong equation ?! 

message: The derivative of Psi equals (A'+iB')Psi!
The equations for the functions A and B are wrong. Plugging in the Ansatz
:\Psi(x) = e^{\Phi(x)}
:\Phi'(x) = A(x) + i B(x) 
into the Schrödinger equation leads to
:A + A'^2 - B'^2 = \frac{2m}{\hbar^2}(V-E)
:B +2A' B' = 0
. —The preceding unsigned comment was added by Matrix1329 (talk • contribs) 11:06, 6 January 2007 (UTC)
replies: text: You seem to working with \phi(x) = A(x) + i B(x) rather than the stated \phi ' (x) = A(x) + i B(x).  That's why you have second derivatives of A and B running around.  — Laura Scudder ☎ 14:36, 1 December 2007 (UTC)
thread_title:  Wrong equation! 

message: This page provides a lot of maths, suited more to a physics textbook and not an encyclopedia.
I'm not saying anything should be removed, but simpler descriptions of the concepts should ideally be provided to those not of a physics-related background. LaudanumCoda 14:50, 10 May 2007 (UTC)
thread_title:  Lacking basics 

message: I think it should be added the WKB formulation for more than one dimension when SE ain't separable , for example whenever you have the potential  V(x,y,z)  in 3-D of the form V=xyz so you need to evaluate the solution using WKB approach, i think Einstein and others estudied this problem but not sure --85.85.100.144 11:31, 26 June 2007 (UTC)
thread_title: Higher Dimension?

message: I added some details of the WKB method and an example from Bender and Orszag. I can be contacted at [redacted] (at) gmail if you think the article still lacks clarity. (Or if you want to thank me for enabling you to do your Applied Math 201 problem set. I'm talking to you, Harvard students.)
--140.247.248.31 (talk) 17:53, 26 November 2007 (UTC)
thread_title:  Added specifics 

message: In: , p.228, there is an account on the history of the WKBJ method. References therein are:
*Francesco Carlini (1817). "Richerche sulla convergenza della serie che serva aal soluzione del problema di Keplero". Milano.
*Joseph Liouville (1837). "Sur le développement des foncttions et séries ...". Journal de Mathématiques Pures et Appliquées 1:16-35.
*George Green (1837). "On the motion of waves in a variable canal of small depth and width". Transactions of the Cambridge Philosophical Society 6:457-462.
*Lord Rayleigh (1912). "On the propagation of waves through a stratified medium, with special reference to the question of reflection". Proceedings of the royal Society London, Series A 86:207-226.
*Richard Gans (1915). "Fortplantzung des Lichts durch ein inhomogenes Medium". Annalen der Physik [4] 47:709-736.
Liouville (1837) and Green (1837) are credited by Olver as the ones who developed the method. Further, in the same historical account by Olver, he cites Jeffreys (1953), who refers to Gans (1915) and (to a lesser extend) Lord Rayleigh (1912) as earlier accounts of the method. -- Kraaiennest (talk) 02:10, 25 January 2008 (UTC)
thread_title: History

message: The abbreviation JWKB has been introduced, to replace WKBJ. I did a Google Scholar search to get an indication on the use of the various forms:
* "WKB approximation": 15500 hits
* "JWKB  approximation": 1030 
* "WKBJ approximation" : 834
* "WBK approximation" : 57
* "BWK approximation" : 33
* "BWKJ approximation" : none, but Google books finds one
* "Wentzel-Kramers-Brillouin approximation" : 529
* "Jeffreys-Wentzel-Kramers-Brillouin approximation" : 12
* "Wentzel-Kramers-Brillouin-Jeffreys approximation" : 7
WKB is by far the most used expression for the method, while JWKB and WKBJ are both quite often used. To my opinion, this should be reflected somehow in the article. -- Crowsnest (talk) 08:43, 18 March 2009 (UTC)
thread_title:  Abbreviation alternatives 

message: https://archive.org/stream/ComptesRendusAcademieDesSciences0183/ComptesRendusAcadmieDesSciences-Tome183-Juillet-dcembre1926#page/n23/mode/2up --217.226.78.134 (talk) 17:29, 14 January 2016 (UTC)
thread_title:  link to reference 

message: Hello. I originally intended to append 'validity of WKB' to the article but ended up rewriting and changing variables to match with the rest of the article. Although, I retained as much of the original article as possible and don't think I left out any detail, my apologies to any prior contributors who find this process disruptive. 
Please consider sharing your criticism here first before choosing to revert article for any reason. I recommend we also give it a little time for others to share their views. Constructive feedback is always appreciated. Thank you!
For reference, this was the state of article before and then after. EditingPencil (talk) 12:00, 21 November 2023 (UTC)
thread_title:  Regarding recent changes