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I just removed the long paragraph on WKB's relationship to Feynman diagrams because it was rather unclear (I'm a physics grad student and couldn't tell what it was trying to say) and also seemed to belong more to the article on One-loop Feynman diagrams rather than this page. Laura Scudder 21:48, 23 Feb 2005 (UTC)
Shouldn't the equation be
rather than
?
See, e.g., http://webpages.ursinus.edu/lriley/courses/p212/lectures/node37.html
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)
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)
Much nicer now, thanks !
Ok so long story short, I just spent 30 minutes writing out the WKB method for the tunneling article and, stupid me, I don't think to see if it is already done. However. This article is missing well over half of the solution. I am going to take what I just wrote and fill in all of the missing parts. —Preceding unsigned comment added by C h fleming ( talk • contribs) 08:11, 27 October 2005
I'd like to add some discussion on the relationship between the WKB method and action, but I'm not sure to what extent this would clutter the article. I at least alluded to such a connection. Also, if memory serves, there was a similiar method to the WKB method used in classical EM, but I know nothing of this. Can anyone expand on this or at least verify? Threepounds 05:52, 27 November 2005 (UTC)
The instanton method in QFT is analogous to the WKB method. See e.g.
here.
Count Iblis
14:01, 3 December 2005 (UTC)
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)
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)
It seems that there's an error in the connection formula expressed in terms of Bessel functions. The dimension of the parameter should be judging from the simplified differential equation near the turning point . The term () inside the Bessel functions is supposed to be dimensionless but it's not. Could someone check this point? By the way, this DE can be cast into the form , the Airy DE. So, the solution can also be expressed by a linear combination of the two Airy functions: . —Preceding unsigned comment added by 24.59.193.0 ( talk • contribs) 04:01, 8 March 2006
While WKB was invented to solve Schrodingers equation, its widely used to solve other wave problems of the form
where k varies slowly on the scale of a one wavelength.
This should be mentioned somewhere, and the derivation of the solution, with
I think the page need to be rewritten along the lines of the Non-QM comment at the bottom. The mathematics of the method is very general and obscured by the extra notation h, E V etc. This would make the method easy to understand and to apply to particular cases. The connection to tunneling should be put in a separate page. There is no need to mention Bessel functions at all. The solution is neater in Airy functions and the Airy function page can link to Bessel functions. I am happy to rewrite the page, I'm an applied mathematician at Cambridge, but do not want to make any changes until other people have given their opinions. Jim McElwaine 16:53, 27 April 2006 (UTC)
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)
The derivative of Psi equals (A'+iB')Psi! The equations for the functions A and B are wrong. Plugging in the Ansatz
into the Schrödinger equation leads to
. —The preceding unsigned comment was added by Matrix1329 ( talk • contribs) 11:06, 6 January 2007 (UTC).
Matrix1329 11:09, 6 January 2007 (UTC)
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)
This is a topic which one would meet in the final year of a physics undergrad degree. Might be difficult to clearly give a good idea. 82.16.99.131 ( talk) 10:12, 4 November 2008 (UTC)
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 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)
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)
In: Olver, Frank J. W. (1974). Asymptotics and Special Functions. Academic Press. ISBN 0-12-525850-X., p.228, there is an account on the history of the WKBJ method. References therein are:
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)
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 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)
https://archive.org/stream/ComptesRendusAcademieDesSciences0183/ComptesRendusAcadmieDesSciences-Tome183-Juillet-dcembre1926#page/n23/mode/2up -- 217.226.78.134 ( talk) 17:29, 14 January 2016 (UTC)
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)