WordNet

give numbers to; "You should number the pages of the thesis"
place a limit on the number of (同)keep_down
a concept of quantity involving zero and units; "every number has a unique position in the sequence"
the property possessed by a sum or total or indefinite quantity of units or individuals; "he had a number of chores to do"; "the number of parameters is small"; "the figure was about a thousand" (同)figure
a clothing measurement; "a number 13 shoe"
an item of merchandise offered for sale; "she preferred the black nylon number"; "this sweater is an all-wool number"
a numeral or string of numerals that is used for identification; "she refused to give them her Social Security number" (同)identification number
a select company of people; "I hope to become one of their number before I die"
the grammatical category for the forms of nouns and pronouns and verbs that are used depending on the number of entities involved (singular or dual or plural); "in English the subject and the verb must agree in number"
enumerate; "We must number the names of the great mathematicians" (同)list
an undulating curve (同)undulation
a persistent and widespread unusual weather condition (especially of unusual temperatures); "a heat wave"
set waves in; "she asked the hairdresser to wave her hair"
a movement like that of a sudden occurrence or increase in a specified phenomenon; "a wave of settlers"; "troops advancing in waves"
one of a series of ridges that moves across the surface of a liquid (especially across a large body of water) (同)moving ridge
(physics) a movement up and down or back and forth (同)undulation
the act of signaling by a movement of the hand (同)waving, wafture
a hairdo that creates undulations in the hair
something that rises rapidly; "a wave of emotion swept over him"; "there was a sudden wave of buying before the market closed"; "a wave of conservatism in the country led by the hard right"
so frightened as to be unable to move; stunned or paralyzed with terror; petrified; "too numb with fear to move"
make numb or insensitive; "The shock numbed her senses" (同)benumb, blunt, dull
a member of the womens reserve of the United States Navy; originally organized during World War II but now no longer a separate branch

PrepTutorEJDIC

〈U〉〈C〉(数えて得られる)『数,数量』 / 〈C〉(概念としての)『数,数字』 / 〈C〉『番号』 / 〈C〉(演奏会や演劇の)番組,出し物;曲目 / 〈C〉(雑誌の)号 / 〈U〉(文法で)数(すう) / 《複数形で》数の上の優勢 / 《複数形で》算数 / 〈C〉《単数形で》《話》(商品としての)洋服の1点;商品,売り物 / 〈C〉《単随形で》《俗》女の子 / …‘を'数える / (…の中に,…として)…‘を'含める,加える《+『among』(『with, as』)+『名』》 / …‘に'番号をつける / …‘の'数となる / 《しばしば受動態で》…‘の'数を制限する / 総計(…に)なる《+『in』+『名』〈数〉》
(前後左右・上下に)『揺れる』,ひらめく,ひらひらする / (波形に)『起伏する』,うねる / (手・旗などを振って)『合図する』,手を振る;(…のために,…に向かって)手を振る《+in(to, at)+名》 / (に向かって)‘…を'振る,揺り動かす,ひらめかす《+名+at+名》 / 《方向を表す副詞[句]を伴って》(手・旗などを振って)〈人〉‘に'『合図する』 / ‘…を'起伏させる,うねらせる:〈頭髪〉‘を'ウエーブさせる / 『波』,波浪 / (…の)『波のような動き』,うねり《+of+名》 / (感情・景気などの一時的な)高まり,強まり;(寒暑の)急激な波《+of+名》 / (手・旗などを)振ること,振ってする合図;(…を)振ること《+of+名》 / (髪の)縮れ,ウエーブ / (光・音・電気などの)波
麻痺(まひ)した,感覚を失った,しびれた / …‘の'感覚を失わせる,‘を'しびれさせる
数学,数学 / (人員などの)数の優勢 / 《米》《the~》=numbers game / 《古》詞句,韻文

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2014/05/30 12:00:59」(JST)

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In the physical sciences, the wavenumber (also wave number) is the spatial frequency of a wave, either in cycles per unit distance or radians per unit distance. It can be envisaged as the number of waves that exist over a specified distance (analogous to frequency being the number of cycles or radians per unit time).

Because of the use of this term in applied physics, including spectroscopy, often the reference distance should be assumed to be cm. For example, a particle's energy may be given as a wavenumber in cm⁻¹, which strictly speaking is not a unit of energy. However if one assumes this corresponds to electromagnetic radiation, then it can be directly converted to any unit of energy, e.g. 1 cm⁻¹ implies 1.23984×10⁻⁴ eV and 8065.54 cm⁻¹ implies 1 eV.^[1]

In multidimensional systems, the wavenumber is also the magnitude of the wave vector.

Definition

It can be defined as either

, the number of wavelengths per unit distance, where λ is the wavelength, sometimes termed the spectroscopic wavenumber, or
,the number of wavelengths per 2π units of distance, sometimes termed the angular or circular wavenumber, but more often simply wavenumber.

Its usual symbols are , , σ or k, the first three used for one definition, the last for another. It has dimensions of reciprocal length, so its SI unit is m⁻¹ and cgs unit cm⁻¹ (in this context formerly called the kayser, after Heinrich Kayser).

For electromagnetic radiation in vacuum, wavenumber is proportional to frequency and to photon energy. Because of this, wavenumbers are used as a unit of energy in spectroscopy. In the SI units, wavenumber is expressed in units of reciprocal meters (m⁻¹), but in spectroscopy it is usual to give wavenumbers in reciprocal centimeters (cm⁻¹). The angular wavenumber is expressed in radians per meter (rad·m⁻¹).

In wave equations

In general, the angular wavenumber (i.e. the magnitude of the wave vector) is given by

where is the frequency of the wave, is the wavelength, is the angular frequency of the wave, and v_p is the phase velocity of the wave. The dependence of the wavenumber on the frequency (or more commonly the frequency on the wavenumber) is known as a dispersion relation.

For the special case of an electromagnetic wave in vacuum, where v_p = c, k is given by

where E is the energy of the wave, ħ is the reduced Planck constant, and c is the speed of light in a vacuum.

For the special case of a matter wave, for example an electron wave, in the non-relativistic approximation:

Here p is the momentum of the particle, m is the mass of the particle, E is the kinetic energy of the particle, and ħ is the reduced Planck's constant.

Wavenumber is also used to define the group velocity.

In spectroscopy

In spectroscopy, the wavenumber of electromagnetic radiation is defined as

where λ is the wavelength of the radiation.

The historical reason for using this quantity is that it proved to be convenient in the analysis of atomic spectra. Wavenumbers were first used in the calculations of Johannes Rydberg in the 1880s. The Rydberg–Ritz combination principle of 1908 was also formulated in terms of wavenumbers. A few years later spectral lines could be understood in quantum theory as differences between energy levels, energy being proportional to wavenumber, or frequency. However, spectroscopic data kept being tabulated in terms of wavenumber rather than frequency or energy, since spectroscopic instruments are typically calibrated in terms of wavelength, independent of the value for the speed of light or Planck's constant.

For example, the wavenumbers of the emissions lines of hydrogen atoms are given by

where R is the Rydberg constant and n_i and n_f are the principal quantum numbers of the initial and final levels, respectively (n_i is greater than n_f for emission).

A wavenumber can be converted into energy E via Planck's relation:

It can also be converted into frequency via

where is the frequency, and c_n is the speed of light in the medium.

In colloquial usage, the unit cm⁻¹ is sometimes referred to as a "wavenumber",^[2] which confuses the name of a quantity with that of a unit. Furthermore, spectroscopists often express a quantity proportional to the wavenumber, such as frequency or energy, in cm⁻¹ and leave the appropriate conversion factor as implied. Consequently, a phrase such as "the energy is 300 wavenumbers" should be interpreted or restated as "the energy corresponds to a wavenumber of 300 cm⁻¹." (Analogous statements hold true for the unit m⁻¹.)

References

^ NIST Reference on Constants, Units and Uncertainty (CODATA 2010), specifically 100/m and 1 eV. Retrieved April 25, 2013.
^ See for example,
- Fiechtner, G. (2001). "Absorption and the dimensionless overlap integral for two-photon excitation". Journal of Quantitative Spectroscopy and Radiative Transfer 68 (5): 543. Bibcode:2001JQSRT..68..543F. doi:10.1016/S0022-4073(00)00044-3.
- US 5046846, Ray, James C. & Asari, Logan R., "Method and apparatus for spectroscopic comparison of compositions", published 1991-09-10
- "Boson Peaks and Glass Formation". Science 308 (5726): 1221. 2005. doi:10.1126/science.308.5726.1221a.

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