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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). In multidimensional systems, the wavenumber is the magnitude of the wave vector. Multiplied by Planck's constant, it is the momentum of a wave, and therefore is employed in all wave mechanics, including quantum mechanics, electrodynamics, etc. The space of wave vectors is called reciprocal space or momentum space and spans 3 dimensions orthogonal to real space, spanning the 6-dimensional phase space, which also describes classical mechanics. Wave numbers and wave vectors play an essential role in optics and the physics of wave scattering, such as X-ray diffraction, neutron diffraction, and elementary particle physics. Wavenumber can be used to specify quantities other than spatial frequency. In optical spectroscopy, it is often used as a unit of temporal frequency assuming a certain speed of light. In this context, it is the number of ''cycles''—not radians—per unit length, and the reference distance should be assumed to be cm. In the same domain, wavenumber can also be used as a unit of energy; 1 cm−1 of energy is the amount of energy in a single photon with a wavelength of 1 cm, the conversion being done using Planck's relation. For example, 1 cm−1 implies 1.23984×10−4 eV and 8065.54 cm−1 implies 1 eV.〔(NIST Reference on Constants, Units and Uncertainty (CODATA 2010) ), specifically (100/m ) and (1 eV ). Retrieved April 25, 2013.〕 ==Definition== It can be defined as either: * , the number of wavelengths per unit distance (equivalently, the number of cycles per wavelength), where ''λ'' is the wavelength, sometimes termed the spectroscopic wavenumber, or * ,the number of radians per unit distance, sometimes termed the angular wavenumber or circular wavenumber, but more often simply ''wavenumber''. There are four total symbols for wavenumber. Under the first definition either , , or ''σ'' may be used; for the second, ''k'' should be used. When wavenumber is represented by the symbol , a frequency is still being represented, albeit indirectly. As described in the spectroscopy section, this is done through the relationship , where s is a frequency in hertz. This is done for convenience as frequencies tend to be very large. It has dimensions of reciprocal length, so its SI unit is the reciprocal of meters (m−1). In spectroscopy it is usual to give wavenumbers in cgs unit, i.e., reciprocal centimeters (cm−1); in this context the wavenumber was formerly called the ''kayser'', after Heinrich Kayser. The angular wavenumber may be expressed in radians per meter (rad·m−1), or as above, since the radian is dimensionless. 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. 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「wavenumber」の詳細全文を読む スポンサード リンク
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