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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Planck constant ： ウィキペディア英語版 Planck constant The Planck constant (denoted , also called Planck's constant) is a physical constant that is the quantum of action, central in quantum mechanics. First recognized in 1900 by Max Planck, it was originally the proportionality constant between the minimal increment of energy, , of a hypothetical electrically charged oscillator in a cavity that contained black body radiation, and the frequency, , of its associated electromagnetic wave. In 1905 the value , the minimal energy increment of a hypothetical oscillator, was theoretically associated by Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called the photon. The Planck–Einstein relation connects the particulate photon energy with its associated wave frequency : :$E\; =\; h\; \backslash nu$ This energy is extremely small in terms of ordinary experience. Since the frequency , wavelength , and speed of light are related by $\backslash nu\; =\; \backslash frac$, the relation can also be expressed as :$E\; =\; \backslash frac\; .$ This leads to another relationship involving the Planck constant. With denoting the linear momentum of a particle (not only a photon, but other fine particles as well), the de Broglie wavelength of the particle is given by :$\backslash lambda\; =\; \backslash frac\; .$ In applications where it is natural to use the angular frequency (i.e. where the frequency is expressed in terms of radians per second instead of cycles per second or hertz) it is often useful to absorb a factor of into the Planck constant. The resulting constant is called the reduced Planck constant or Dirac constant. It is equal to the Planck constant divided by , and is denoted (pronounced "h-bar"): :$\backslash hbar\; =\; \backslash frac\; .$ The energy of a photon with angular frequency , where , is given by :$E\; =\; \backslash hbar\; \backslash omega\; ,$ while its linear momentum relates to :$p\; =\; \backslash hbar\; k\; ,$ where ''k'' is a wavenumber. In 1923, Louis de Broglie generalized the Planck–Einstein relation by postulating that the Planck constant represents the proportionality between the momentum and the quantum wavelength of not just the photon, but the quantum wavelength of any particle. This was confirmed by experiments soon afterwards. This holds throughout quantum theory, including electrodynamics. These two relations are the temporal and spatial component parts of the special relativistic expression using 4-Vectors. :$P^\backslash mu\; =\; \backslash left(\backslash frac,\; \backslash vec\backslash right)\; =\; \backslash hbar\; K^\backslash mu\; =\; \backslash hbar\backslash left(\backslash frac,\; \backslash vec\backslash right)$ Classical statistical mechanics requires the existence of (but does not define its value). Eventually, following upon Planck's discovery, it was recognized that physical action cannot take on an arbitrary value. Instead, it must be some multiple of a very small quantity, the "quantum of action", now called the Planck constant. Classical physics cannot explain this fact. In many cases, such as for monochromatic light or for atoms, this quantum of action also implies that only certain energy levels are allowed, and values in between are forbidden. == Value == The Planck constant has dimensions of physical action; these are the same as those of angular momentum, i.e., energy multiplied by time, or momentum multiplied by distance. In SI units, the Planck constant is expressed in joule seconds (J⋅s) or (N⋅m⋅s) or (kg⋅m2⋅s−1). The value of the Planck constant is:〔 :$h\; =\; 6.626\backslash \; 070\backslash \; 040(81)\backslash times\; 10^\backslash text\; =\; 4.135\backslash \; 667\backslash \; 662(25)\backslash times\; 10^\backslash text\; .$ The value of the reduced Planck constant is: :$\backslash hbar\; =\; =\; 1.054\backslash \; 571\backslash \; 800(13)\backslash times\; 10^\backslash text\; =\; 6.582\backslash \; 119\backslash \; 514(40)\backslash times\; 10^\backslash text\; .$ The two digits inside the parentheses denote the standard uncertainty in the last two digits of the value. The figures cited here are the 2014 CODATA recommended values for the constants and their uncertainties. The 2014 CODATA results were made available in June 2015 and represent the best-known, internationally accepted values for these constants, based on all data published as of 31 December 2014. New CODATA figures are normally produced every four years. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Planck constant」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.