Quantization: Difference between revisions
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In [[physics]], '''quantization''', in its original meaning, refers to the fact that the [[energy]] of many [[physical system]]s is not continuous, but discrete—''quantized''. The size of the discrete energy "parcels" is determined by [[Planck's constant]] ''h''. This natural constant (''h'' ≈ 6.626 ×10<sup>−34</sup> Js), is so small that on a macroscopic scale (energies on the order of joules, time intervals on the order of seconds), quantization is a minute effect that can hardly be observed. For all intents and purposes, macroscopic energies are continuous. | In [[physics]], '''quantization''', in its original meaning, refers to the fact that the [[energy]] of many [[physical system]]s is not continuous, but discrete—''quantized''. The size of the discrete energy "parcels" is determined by [[Planck's constant]] ''h''. This natural constant (''h'' ≈ 6.626 ×10<sup>−34</sup> Js), is so small that on a macroscopic scale (energies on the order of joules, time intervals on the order of seconds), quantization is a minute effect that can hardly be observed. For all intents and purposes, macroscopic energies are continuous. | ||
Energy quantization was first introduced in 1900 by [[Max Planck]] in his theory of [[black-body radiation]],<ref>M. Planck, '' | Energy quantization was first introduced in 1900 by [[Max Planck]] in his theory of [[black-body radiation]],<ref>M. Planck, ''Ueber irreversible Strahlungsvorgänge'' [On irreversible radiation events], Annalen der Physik, vol. '''1''', pp. 69–122 (1900) [http://gallica.bnf.fr/ark:/12148/bpt6k15311v.image.r=Annalen+der+Physic.f75.langFR Online]</ref> when he assumed that the walls of a blackbody consist of [[Harmonic oscillator (quantum)|harmonic oscillators]] and that the energies of these oscillators are discrete. He was forced to introduce this assumption in his explanation of the experimentally observed deviations from [[Wien's distribution law]]. Planck did not quantize the black-body radiation itself. [[Electromagnetic radiation]] was quantized five years later by [[Albert Einstein]],<ref>A. Einstein, ''Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt'' [On a heuristic point view regarding the creation and conversion of light], Annalen der Physik, vol. '''17''', pp. 132 - 148, | ||
[http://dx.doi.org/10.1002/andp.19053220607 online]. </ref> who postulated that the electromagnetic field consists of light quanta (energy parcels, that were later called [[photons]]). Einstein's energy parcels are of size ''hν'', where ν is the [[frequency]] of the [[electromagnetic wave]]s. In 1923 [[Louis de Broglie]]<ref>L. de Broglie, ''Waves and Quanta'', Nature, vol. 112, October 13, 1923, p. 540</ref> announced that the [[Energy_(science)#Equivalence_of_energy_and_mass|relativistic kinetic energy]] of material particles is also quantized and derived the consequence that the motion of material particles is wave-like. The very small value of ''h'' explains why the wavelike nature of matter is very difficult to demonstrate on a macroscopic scale. The work of de Broglie inspired [[Erwin Schrödinger]] to postulate a wave equation that describes the motion of very light material particles, such as [[electron]]s.<ref> E. Schrödinger, ''Quantisierung als Eigenwerproblem'' [quantization as eigenvalue problem] Annalen der Physik, Vierte Folge, Band 79, p. 361 (1926) | [http://dx.doi.org/10.1002/andp.19053220607 online]. </ref> who postulated that the electromagnetic field consists of light quanta (energy parcels, that were later called [[photons]]). Einstein's energy parcels are of size ''hν'', where ν is the [[frequency]] of the [[electromagnetic wave]]s. In 1923 [[Louis de Broglie]]<ref>L. de Broglie, ''Waves and Quanta'', Nature, vol. 112, October 13, 1923, p. 540 [http://www.nature.com/physics/looking-back/debroglie/index.html Online]</ref> announced that the [[Energy_(science)#Equivalence_of_energy_and_mass|relativistic kinetic energy]] of material particles is also quantized and derived the consequence that the motion of material particles is wave-like. The very small value of ''h'' explains why the wavelike nature of matter is very difficult to demonstrate on a macroscopic scale. The work of de Broglie inspired [[Erwin Schrödinger]] to postulate a wave equation that describes the motion of very light material particles, such as [[electron]]s.<ref> E. Schrödinger, ''Quantisierung als Eigenwerproblem'' [quantization as eigenvalue problem] Annalen der Physik, Vierte Folge, Band 79, p. 361 (1926) | ||
[http://gallica.bnf.fr/ark:/12148/bpt6k153811.pleinepage.r=Annalen+der+Physic.f373.langEN Online] | [http://gallica.bnf.fr/ark:/12148/bpt6k153811.pleinepage.r=Annalen+der+Physic.f373.langEN Online] | ||
</ref> When [[Schrödinger equation|Schrödinger's wave equation]] is solved with appropriate boundary conditions, energy quantization follows automatically for ''bound systems'' (not for unbound systems where particles come and go to and from infinity). In Schrödinger's theory certain operators play a role that correspond to classical (electromagnetic or mechanical) experimentally observable properties. | </ref> When [[Schrödinger equation|Schrödinger's wave equation]] is solved with appropriate boundary conditions, energy quantization follows automatically for ''bound systems'' (not for unbound systems where particles come and go to and from infinity). In Schrödinger's theory certain operators play a role that correspond to classical (electromagnetic or mechanical) experimentally observable properties. | ||
Revision as of 10:35, 28 November 2009
In physics, quantization, in its original meaning, refers to the fact that the energy of many physical systems is not continuous, but discrete—quantized. The size of the discrete energy "parcels" is determined by Planck's constant h. This natural constant (h ≈ 6.626 ×10−34 Js), is so small that on a macroscopic scale (energies on the order of joules, time intervals on the order of seconds), quantization is a minute effect that can hardly be observed. For all intents and purposes, macroscopic energies are continuous.
Energy quantization was first introduced in 1900 by Max Planck in his theory of black-body radiation,[1] when he assumed that the walls of a blackbody consist of harmonic oscillators and that the energies of these oscillators are discrete. He was forced to introduce this assumption in his explanation of the experimentally observed deviations from Wien's distribution law. Planck did not quantize the black-body radiation itself. Electromagnetic radiation was quantized five years later by Albert Einstein,[2] who postulated that the electromagnetic field consists of light quanta (energy parcels, that were later called photons). Einstein's energy parcels are of size hν, where ν is the frequency of the electromagnetic waves. In 1923 Louis de Broglie[3] announced that the relativistic kinetic energy of material particles is also quantized and derived the consequence that the motion of material particles is wave-like. The very small value of h explains why the wavelike nature of matter is very difficult to demonstrate on a macroscopic scale. The work of de Broglie inspired Erwin Schrödinger to postulate a wave equation that describes the motion of very light material particles, such as electrons.[4] When Schrödinger's wave equation is solved with appropriate boundary conditions, energy quantization follows automatically for bound systems (not for unbound systems where particles come and go to and from infinity). In Schrödinger's theory certain operators play a role that correspond to classical (electromagnetic or mechanical) experimentally observable properties.
Quantization rules
In the second, more modern meaning of the word, quantization means the replacement of classical equations for classical quantities, by quantum mechanical equations for quantum mechanical objects.
References
- ↑ M. Planck, Ueber irreversible Strahlungsvorgänge [On irreversible radiation events], Annalen der Physik, vol. 1, pp. 69–122 (1900) Online
- ↑ A. Einstein, Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt [On a heuristic point view regarding the creation and conversion of light], Annalen der Physik, vol. 17, pp. 132 - 148, online.
- ↑ L. de Broglie, Waves and Quanta, Nature, vol. 112, October 13, 1923, p. 540 Online
- ↑ E. Schrödinger, Quantisierung als Eigenwerproblem [quantization as eigenvalue problem] Annalen der Physik, Vierte Folge, Band 79, p. 361 (1926) Online