Talk:Perturbation theory

Linear combination of atomic orbitals molecular orbital method

I have edited the history section as the LCAO method was introduced by Sir John Lennard-Jones in 1929, not by Fano. However, in what way is this method perturbation theory? What is the unperturbed function? What is the perturbation? I would call it a variational method in contrast to perturbational methods in quantum chemistry. --Bduke 08:06, 10 June 2007 (UTC)

This is explained a bit here. However, variational methods can be used to derive non-perturbative results (i.e. effects that vanish to all orders in perturbation theory). So, in general, variational methods are not equivalent to perturbation theory. Count Iblis 14:23, 10 June 2007 (UTC)

Indeed but LCAO itself is not perturbation theory. It is used in Hartree-Fock theory get the unperturbed reference in methods like MP2. It is the section on LCAO that I think should be removed from this article. LCAO is a variational method, which as you say is not equivalent to perturbation theory. --Bduke 01:12, 11 June 2007 (UTC)

Yes, I agree with removal of that section. I'm not sure if other editors want to give their opinion, so let's wait a few days... Count Iblis 13:05, 12 June 2007 (UTC)

epicycles

The sentence about 17th century epicycles in the history of PT sounds strange to me. In the first place epicycles became less important after Keppler's work of around 1610. In the second place, if epicycles have anything to do with PT, then the origin of PT goes back to Ptolemy (150) and Hipparchos (100 BC). Any expert opinions? In any case a source is indispensable.--P.wormer 09:28, 12 June 2007 (UTC)

In one sense there is nothing either old or new about epicycles, they are merely geometrical analogues of circular functions. As it was expressed by H Godfray in 'An Elementary Treatise on the Lunar Theory' (4th ed 1885) at pp.63-64: our expressions, composed of periodic terms, are nothing more than translations into analytical language of the epicycles of the ancient; (Godfray went on to contrast the modern method of using gravitational theory to derive the periodic functions, as against the narrow repertoire of methods available to the ancients who had to infer their results from laborious observation).Terry0051 (talk) 16:37, 4 March 2009 (UTC)

History

Perturbation theory has its roots in 17th century celestial mechanics, where the theory of epicycles was used to make small corrections to the predicted paths of planets. Curiously, it was the need for more and more epicycles that eventually led to the 16th century Copernican revolution in the understanding of planetary orbits. [The previous sentence is mistaken: it is a common misunderstanding that Copernicus did away with epicycles. However, a close examination of Copernicus' great treatise, the De Revolutionibus reveals that, not only does Copernicus freely employ epicycles, but that he commits many of the same offenses in his planetary models as both he and the Tradition had accused Ptolemy of doing.]PtolemyGalen 17:36, 28 August 2007 (UTC)

Are the dates above (and in the actual article) correct? The wording seems to imply that people were still doing epicycles a century after the Copernican revolution, and that this continuing study of epicyles led (or fed into) perturbation theory. I would have thought that scientists and mathematicians would have given up trying to work with epicycles by the 17th century. Mcswell (talk) 16:15, 29 June 2008 (UTC)

The language in the article is heavily anachronistic (see prochronism): especially where it says "The earliest use of perturbation theory was to deal with the otherwise unsolveable mathematical problems of celestial mechanics: Newton's solution for the orbit of the Moon,...". Problems with this language include the following:

(a) Newton's consideration of the problem of the deviations from undisturbed Keplerian experienced by three bodies moving under their mutual gravitational attractions, (in Bk.I, Prop.66 and its corollaries, in the 'Principia', 1687) was not a 'use of' perturbation theory as one is said to make 'use of' something actually in existence already: rather, Newton gave the first description ever to define or consider such a problem (as recognised for example by expert commentators such as F-F Tisserand, 1894, Traite de Mecanique Celest, e.g. vol 3, ch 3); it set a new agenda for the recognition and investigation of disturbed motion under plural or multiple gravitational attractions, and contributed the first steps to the creation and recognition of perturbation theory as a subject.

(b) It was only much later that the idea 'celestial mechanics' came in, this expression is due to Laplace who greatly extended the reach of the subject, a century after Newton. Newton did not use the word 'dynamics', either: his preferred expression in the Principia was 'rational mechanics': thus, in the words of the Author's Preface in Newton's 'Principia' (1729 English translation): Rational Mechanics will be the science of motions resulting from any forces whatsoever and of the forces required to produce any motions, accurately proposed and demonstrated.Terry0051 (talk) 16:37, 4 March 2009 (UTC)

LINK TO THE WRONG SPANISH VERSION ARTICLE

Hi, just a couple of words to tell the contributors to this article that the "Spanish" link takes to Teoría perturbacional, an article about quantum mechanics, not about mathematics. Someone wanting to correct it? Best wishes, --Mechanismic (talk) 09:47, 31 August 2009 (UTC)

Fixed it, thanks for spotting it. :-) The links are listed at the bottom of the article when you press edit, so it's easy to correct. These errors sometimes creep back via automatic bots if they'r present in other languages as well, but in this case no other language seems to have made the mistake, so we should be safe. EverGreg (talk) 16:06, 31 August 2009 (UTC)

Broken link

Hi, I'd just found a broken link:

• Chapter II: Introduction to perturbation methods by Johan Byström, Lars-Erik Persson, and Fredrik Strömberg

Since I do not understand very well the wikipedia's broken link policy, I just announcing it here. Cheers. Felipebm (talk) 19:54, 22 December 2009 (UTC)

It is still dead, so I just removed the link. It looks like a cache is available at the Wayback Machine, but it doesn't seem crucial to keep it in the External Links (and the Wayback Machine's servers often fail). Maghnus (talk) 21:52, 1 January 2010 (UTC)

Reference for use of Feynman Diagrams in classical mechanics

"Although originally applied only in quantum field theory, such diagrams now find increasing use in any area where perturbative expansions are studied.[citation needed]"

There is a citation that could be added :

http://arxiv.org/abs/hep-th/0605061

Arjun R. Acharya (talk) 09:21, 14 February 2010 (UTC)