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| == '''[[British and American English]]''' == | | {{:{{FeaturedArticleTitle}}}} |
| ''by [[User:Ro Thorpe|Ro Thorpe]] and others <small>([[User:Hayford Peirce|Hayford Peirce]], [[User:John Stephenson|John Stephenson]], [[User:Peter Jackson|Peter Jackson]], [[User:Chris Day|Chris Day]], [[User:Martin Baldwin-Edwards|Martin Baldwin-Edwards]], and [[User:J. Noel Chiappa|J. Noel Chiappa]])</small>''
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| | ==Footnotes== |
| Between '''[[British English]] and [[American English]]''' there are numerous differences in the areas of [[lexis|vocabulary]], [[spelling]], and [[phonology]]. This article compares the forms of British and American speech normally studied by foreigners: the former includes the [[Accent (linguistics)|accent]] known as [[Received Pronunciation]], or RP; the latter uses [[Midland American English]], which is normally perceived to be the least marked American [[dialect]]. Actual speech by educated British and American speakers is more varied, and that of uneducated speakers still more. [[Grammar|Grammatical]] and lexical differences between British and American English are, for the most part, common to all dialects, but there are many regional differences in pronunciation, vocabulary, usage and slang, some subtle, some glaring, some rendering a sentence incomprehensible to a speaker of another variant.
| | {{reflist|2}} |
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| American and British English both diverged from a common ancestor, and the evolution of each language is tied to social and cultural factors in each land. Cultural factors can affect one's understanding and enjoyment of language; consider the effect that [[slang]] and [[double entendre]] have on humour. A joke is simply not funny if the [[pun]] upon which it is based can't be understood because the word, expression or cultural icon upon which it is based does not exist in one's variant of English. Or, a joke may be only partially understood, that is, understood on one level but not on another, as in this exchange from the [[Britcom]] ''[[Dad's Army]]'':
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| Fraser: Did ya hear the story of the old empty barn?
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| Mainwaring: Listen, everyone, Fraser's going to tell a story.
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| Fraser: The story of the old empty barn: well, there was nothing in it!
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| Americans would 'get' part of the joke, which is that a barn that is empty literally has nothing in it. However, in Commonwealth English, 'there's nothing in it' also means something that is trivial, useless or of no significance.
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| But it is not only humour that is affected. Items of cultural relevance change the way English is expressed locally. A person can say "I was late, so I ''Akii-Bua'd'' (from [[John Akii-Bua]], Ugandan hurdler) and be understood all over East Africa, but receive blank stares in [[Australia]]. Even if the meaning is guessed from context, the nuance is not grasped; there is no resonance of understanding. Then again, because of evolutionary divergence; people can believe that they are speaking of the same thing, or that they understand what has been said, and yet be mistaken. Take adjectives such as 'mean' and 'cheap'. Commonwealth speakers still use 'mean' to mean 'parsemonious', Americans understand this usuage, but their first use of the word 'mean' is 'unkind'. Americans use 'cheap' to mean 'stingy', but while Commonwealth speakers understand this, there is a danger that when used of a person, it can be interpreted as 'disreputable' 'immoral' (my grandmother was so ''cheap''). The verb 'to table' a matter, as in a conference, is generally taken to mean 'to defer', in American English, but as 'to place on the table', i.e. to bring up for discussion, in Commonwealth English.
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| English is a flexible and quickly-evolving language; it simply absorbs and includes words and expressions for which there is no current English equivalent; these become part of the regional English. American English has hundreds of loan words acquired from its [[immigration|immigrants]]: these can eventually find their way into widespread use, (''[[spaghetti]]'', ''mañana''), or they can be restricted to the areas in which immigrant populations live. So there can be variances between the English spoken in [[New York City]], [[Chicago]], and [[San Francisco]]. Thanks to Asian immigration, a working-class [[London|Londoner]] asks for a ''cuppa cha'' and receives the tea he requested. This would probably be understood in [[Kampala]] and [[New Delhi]] as well, but not necessarily in [[Boise]], [[Idaho]].
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| Cultural exchange also has an impact on language. For example, it is possible to see a certain amount of Americanization in the British English of the last 50 years. This influence is not entirely one-directional, though, as, for instance, the previously British English 'flat' for 'apartment' has gained in usage among American twenty-somethings. Similarly the American pronunciation of '[[aunt]]' has changed during the last two decades, and it is considered classier to pronounce 'aunt' in the [[Commonwealth]] manner, even for speakers who continue to rhyme 'can't' and 'shan't' with 'ant'. [[Australian English]] is based on the language of the Commonwealth, but has also blended indigenous, immigrant and American imports.
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| Applying these same phenomena to the rest of the English-speaking world, it becomes clear that though the "official" differences between Commonwealth and American English can be more or less delineated, the English language can still vary greatly from place to place.
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| ''[[British and American English|.... (read more)]]''
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In computational molecular physics and solid state physics, the Born-Oppenheimer approximation is used to separate the quantum mechanical motion of the electrons from the motion of the nuclei. The method relies on the large mass ratio of electrons and nuclei. For instance the lightest nucleus, the hydrogen nucleus, is already 1836 times heavier than an electron. The method is named after Max Born and Robert Oppenheimer[1], who proposed it in 1927.
Rationale
The computation of the energy and wave function of an average-size molecule is a formidable task that is alleviated by the Born-Oppenheimer (BO) approximation.The BO approximation makes it possible to compute the wave function in two less formidable, consecutive, steps. This approximation was proposed in the early days of quantum mechanics by Born and Oppenheimer (1927) and is indispensable in quantum chemistry and ubiquitous in large parts of computational physics.
In the first step of the BO approximation the electronic Schrödinger equation is solved, yielding a wave function depending on electrons only. For benzene this wave function depends on 126 electronic coordinates. During this solution the nuclei are fixed in a certain configuration, very often the equilibrium configuration. If the effects of the quantum mechanical nuclear motion are to be studied, for instance because a vibrational spectrum is required, this electronic computation must be repeated for many different nuclear configurations. The set of electronic energies thus computed becomes a function of the nuclear coordinates. In the second step of the BO approximation this function serves as a potential in a Schrödinger equation containing only the nuclei—for benzene an equation in 36 variables.
The success of the BO approximation is due to the high ratio between nuclear and electronic masses. The approximation is an important tool of quantum chemistry, without it only the lightest molecule, H2, could be handled; all computations of molecular wave functions for larger molecules make use of it. Even in the cases where the BO approximation breaks down, it is used as a point of departure for the computations.
Historical note
The Born-Oppenheimer approximation is named after M. Born and R. Oppenheimer who wrote a paper
[Annalen der Physik, vol. 84, pp. 457-484 (1927)] entitled: Zur Quantentheorie der Molekeln (On the Quantum Theory of Molecules). This paper describes the separation of electronic motion, nuclear vibrations, and molecular rotation. A reader of this paper who expects to find clearly delineated the BO approximation—as it is explained above and in most modern textbooks—will be disappointed. The presentation of the BO approximation is well hidden in Taylor expansions (in terms of internal and external nuclear coordinates) of (i) electronic wave functions, (ii) potential energy surfaces and (iii) nuclear kinetic energy terms. Internal coordinates are the relative positions of the nuclei in the molecular equilibrium and their displacements (vibrations) from equilibrium. External coordinates are the position of the center of mass and the orientation of the molecule. The Taylor expansions complicate the theory tremendously and make the derivations
very hard to follow. Moreover, knowing that the proper separation of vibrations and rotations was not achieved in this work, but only eight years later [by C. Eckart, Physical Review, vol. 46, pp. 383-387 (1935)] (see Eckart conditions), chemists and molecular physicists are not very much motivated to invest much effort into understanding the work by Born and Oppenheimer, however famous it may be. Although the article still collects many citations each year, it is safe to say that it is not read anymore, except maybe by historians of science.