https://www.wikidoc.org/index.php?title=De_Broglie_hypothesis&feed=atom&action=historyDe Broglie hypothesis - Revision history2021-07-25T22:53:30ZRevision history for this page on the wikiMediaWiki 1.35.0https://www.wikidoc.org/index.php?title=De_Broglie_hypothesis&diff=672373&oldid=prevWikiBot: Bot: Automated text replacement (-{{SIB}} + & -{{EH}} + & -{{EJ}} + & -{{Editor Help}} + & -{{Editor Join}} +)2012-08-09T00:30:27Z<p>Bot: Automated text replacement (-{{SIB}} + & -{{EH}} + & -{{EJ}} + & -{{Editor Help}} + & -{{Editor Join}} +)</p>
<p><b>New page</b></p><div><br />
<br />
{{lowercase|de Broglie hypothesis}}<br />
In [[physics]], the '''de Broglie hypothesis''' (pronounced /brœj/, as French breuil, close to "broy") is the statement that all [[matter]] (any object) has a [[wave]]-like nature ([[wave-particle duality]]). The '''de Broglie relations''' show that the [[wavelength]] is [[inversely proportional]] to the [[momentum]] of a particle and that the [[frequency]] is directly proportional to the particle's [[kinetic energy]]. The hypothesis was advanced by [[Louis de Broglie]] in [[1924]] in his PhD thesis<ref>L. de Broglie, ''Recherches sur la théorie des quanta'' (Researches on the quantum theory), Thesis (Paris), 1924; L. de Broglie, ''Ann. Phys.'' (Paris) '''3''', 22 (1925).<br />
Reprinted in ''Ann. Found. Louis de Broglie'' '''17''' (1992) p. 22.</ref>; he was awarded the [[Nobel Prize for Physics]] in [[1929]] for this work, which made him the first person to receive a Nobel Prize on a PhD thesis. <br />
<br />
==Historical context==<br />
After strides made by [[Max Planck]] (1858-1947) and [[Albert Einstein]] (1879-1955) in understanding the behavior of electrons and what would be known as quantum physics, [[Niels Bohr]] (1885-1962) began (among other things) trying to explain how electrons behave. He came up with new fundamental ideas about electrons and mathematically derived the [[Rydberg equation]], an equation that was discovered only through trial and error. This equation explains the [[energy|energies]] of the [[Spectral line|light emitted]] when hydrogen gas is compressed and electrified (similar to neon signs, but with hydrogen in this case). Unfortunately, his model only worked for the hydrogen-atom-configuration, but his ideas were so revolutionary that they broke up the classical view of electrons' behavior and paved the way for fresh new ideas in what would become quantum physics and quantum mechanics.<br />
<br />
[[Louis de Broglie]] (1892-1987) tried to expand on Bohr's ideas, and he pushed for their application beyond hydrogen. In fact he looked for an equation which could explain the wavelength characteristics of all matter. His equation was not proved experimentally until a few years later{{Fact|date=August 2007}}. Nevertheless, his hypothesis would hold true for both electrons and for everyday objects. In de Broglie's equation an electron's wavelength will be a function of [[Planck's constant]] (<math>6.626 \times 10^{-34}</math> [[joule]]-seconds) divided by the object's [[Momentum#Momentum_in_Newtonian_mechanics|momentum]] (nonrelativistically, its [[mass]] multiplied by its [[velocity]]). When this momentum is very large (relative to Planck's constant), then an object's wavelength is very small. This is the case with every-day objects, such as a person. Given the enormous momentum of a person compared with the very tiny Planck constant, the wavelength of a person would be so small (on the order of <math>10^{-35}</math> meters or smaller) as to be undetectable by any current measurement tools. On the other hand, many small particles (such as typical electrons in everyday materials) have a very low momentum compared to macroscopic objects. In this case, the de Broglie wavelength may be large enough that the particle's wave-like nature gives observable effects.<br />
<br />
The wave-like behavior of small-momentum particles is analogous to that of light. As an example, [[electron microscopes]] use electrons, instead of light, to see very small objects. Since electrons typically have more momentum than photons, their de Broglie wavelength will be smaller, resulting in a greater spatial resolution.<br />
<br />
==The de Broglie relations==<br />
The first de Broglie equation relates the wavelength <math>\lambda</math> to the particle momentum <math>~p~</math> as<br />
<br />
:<math>\lambda = \frac{h}{p} = \frac {h}{\gamma mv} = \frac {h}{mv} \sqrt{1 - \frac{v^2}{c^2}}</math><br />
<br />
where <math>~h~</math> is [[Planck's constant]], <math>~m~</math> is the particle's [[rest mass]], <math>~v~</math> is the particle's [[velocity]], <math>~\gamma~</math> is the [[Lorentz factor]], and <math>~c~</math> is the [[speed of light]] in a vacuum.<br />
<br />
The greater the energy, the larger the [[frequency]] and the shorter (smaller) the wavelength. Given the relationship between wavelength and frequency, it follows that short wavelengths are more energetic than long wavelengths. The second de Broglie equation relates the frequency of the wave associated to a particle to the total energy of the particle such that<br />
<br />
:<math>f = \frac{E}{h} = \frac{\gamma\,mc^2}{h} = \frac {1}{\sqrt{1 - \frac{v^2}{c^2}}} \cdot \frac{mc^2}{h}</math><br />
<br />
where <math>~f~</math> is the frequency and <math>~E~</math> is the total energy. The two equations are often written as<br />
<br />
:<math>p = \hbar k</math><br />
:<math>E = \hbar \omega</math><br />
<br />
where <math>~\hbar=h/(2\pi)~</math> is the reduced [[Planck's constant]] (also known as '''Dirac's constant''', pronounced "h-bar"), <math>~k~</math> is the [[wavenumber#In wave equations|wavenumber]], and <math>~\omega~</math> is the [[angular frequency]].<br />
<br />
See the article on [[group velocity]] for detail on the argument and derivation of the de Broglie relations.<br />
<br />
==Experimental confirmation==<br />
===Elementary particles===<br />
In 1927 at Bell Labs, [[Clinton Davisson]] and [[Lester Germer]] fired slow-moving [[electrons]] at a [[crystalline]] [[nickel]] target. The angular dependence of the reflected electron intensity was measured, and was determined to have the same [[diffraction|diffraction pattern]] as those predicted by [[William Lawrence Bragg|Bragg]] for [[X rays|X-Rays]]. Before the acceptance of the de Broglie hypothesis, diffraction was a property that was thought to be only exhibited by waves. Therefore, the presence of any [[diffraction]] effects by matter demonstrated the wave-like nature of matter. When the de Broglie wavelength was inserted into the [[Bragg's law|Bragg condition]], the observed diffraction pattern was predicted, thereby experimentally confirming the de Broglie hypothesis for electrons.<br />
<br />
This was a pivotal result in the development of [[quantum mechanics]]. Just as [[Arthur Compton]] demonstrated the particle nature of light, the [[Davisson-Germer experiment]] showed the wave-nature of matter, and completed the theory of wave-particle duality. For [[physicists]] this idea was important because it means that not only can any particle exhibit wave characteristics, but that one can use [[wave equation]]s to describe phenomena in matter if one uses the de Broglie wavelength.<br />
<br />
Since the original Davisson-Germer experiment for electrons, the '''de Broglie hypothesis''' has been confirmed for other [[elementary particles]].<br />
<br />
===Neutral atoms===<br />
Experiments with [[Fresnel diffraction]]<ref name="doak">{{cite journal| url=http://prola.aps.org/abstract/PRL/v83/i21/p4229_1<br />
| author=R.B.Doak | coauthors=R.E.Grisenti, S.Rehbein, G.Schmahl, J.P.Toennies2, and Ch. Wöll<br />
| title=Towards Realization of an Atomic de Broglie Microscope: Helium Atom Focusing Using Fresnel Zone Plates<br />
| journal=[[Physical Review Letters|PRL]] | volume=83 | pages=4229-4232 | year=1999 }}</ref><br />
and [[specular reflection]] <ref name="sh">{{cite journal | url=http://prola.aps.org/abstract/PRL/v86/i6/p987_1<br />
| author= F. Shimizu | title=Specular Reflection of Very Slow Metastable Neon Atoms from a Solid Surface<br />
| journal=[[Physical Review Letters|PRL]]| volume=86| pages=987-990 | year=2000<br />
}}</ref><ref name="zeno">{{cite journal<br />
|comment=7<br />
| url=http://annex.jsap.or.jp/OSJ/opticalreview/TOC-Lists/vol12/12e0363tx.htm<br />
| author= D. Kouznetsov<br />
| coauthors= H. Oberst<br />
| title=Reflection of Waves from a Ridged Surface and the Zeno Effect<br />
| journal=[[Optical Review]]<br />
| volume=12<br />
| pages=1605-1623<br />
| year=2005<br />
}}</ref><br />
of neutral atoms<br />
confirm the application of the De Broglie hypothesis to atoms, i.e. the existence of '''atomic waves''' which undergo <br />
[[diffraction]], [[interference]] and allow [[quantum reflection]] by the tails of the attractive potential<br />
<ref name="Fri"><br />
{{cite journal <br />
|author=H.Friedrich<br />
|coauthors=G.Jacoby, C.G.Meister<br />
|journal=[[Physical Review A|PRA]]<br />
|title=quantum reflection by Casimir–van der Waals potential tails<br />
|year=2002<br />
|volume=65<br />
|page=032902<br />
|url=http://prola.aps.org/abstract/PRA/v65/i3/e032902<br />
}}<br />
</ref>.<br />
This effect has been used to demonstrate atomic [[holography]]<br />
<ref name="holo">{{cite journal<br />
| title = Reflection-Type Hologram for Atoms<br />
| author = Shimizu| coauthors=J.Fujita<br />
| journal = [[Physical Review Letters|PRL]]<br />
| volume = 88 | number = 12<br />
| pages = 123201 | year = 2002<br />
|url=http://prola.aps.org/abstract/PRL/v88/i12/e123201<br />
| doi = 10.1103/PhysRevLett.88.123201<br />
| publisher = [[American Physical Society]]<br />
}}</ref>, and it may allow the construction of an atom probe imaging system with nanometer resolution <ref name="nanoscope">{{cite journal<br />
| url=http://stacks.iop.org/0953-4075/39/1605<br />
| author= D. Kouznetsov<br />
| coauthors=H. Oberst, K. Shimizu, A. Neumann, Y. Kuznetsova, J.-F. Bisson, K. Ueda, S. R. J. Brueck<br />
| title=Ridged atomic mirrors and atomic nanoscope<br />
| journal=[[Journal of Physics B|JOPB]]<br />
| volume=39<br />
| pages=1605-1623<br />
| year=2006<br />
}}</ref>.<br />
The description of these phenomena is based on the wave properties of neutral atoms, confirming the '''de Broglie hypothesis'''.<br />
<br />
===Waves of molecules===<br />
Recent experiments even confirm the relations for molecules and even [[macromolecules]], which are normally considered too large to undergo quantum mechanical effects. In [[1999]], a research team in [[Vienna]] demonstrated diffraction for molecules as large as [[fullerenes]]<ref>{{cite journal| title=Wave-particle duality of C60| first=M.| last=Arndt| coauthors=O. Nairz, [[Julian Voss-Andreae|J. Voss-Andreae]], C. Keller, G. van der Zouw, [[Anton Zeilinger|A. Zeilinger]]| journal=Nature| volume=401| pages=680-682| month=14 October| year=1999| doi=10.1038/44348}}</ref>.<br />
<br />
In general, the '''De Broglie hypothesis''' is expected to apply to any well isolated object.<br />
<br />
==Spatial Zeno effect==<br />
The De Broglie hypothesis leads to the spatial version of the [[Zeno effect]]. If an object (particle) is observed with frequency <math>~\Omega\gg\omega~</math><br />
in a half-space (say, <math>~y<0~</math>), then this observation prevents the particle, which stays in the half-space <math>~y>0~</math> from entry into this half-space <br />
<math>~y<0~</math>. Such an "observation" can be realized with a set of rapidly moving absorbing ridges, filling one half-space. In the system of coordinates related to <br />
the ridges, this phenomenon appears as a [[specular reflection]] of a particle from a [[ridged mirror]], assuming the grazing incidence (small values of the [[grazing angle]]).<br />
Such a ridged mirror is universal; while we consider the idealised "absorption" of the de Broglie wave at the ridges, the reflectivity is determined by wavenumber <math>~k~</math> and does not depend on other properties of a particle.<br />
<ref name="zeno">{{cite journal<br />
|comment=7<br />
| url=http://annex.jsap.or.jp/OSJ/opticalreview/TOC-Lists/vol12/12e0363tx.htm<br />
| author= D.Kouznetsov<br />
| coauthors= H.Oberst<br />
| title=Reflection of Waves from a Ridged Surface and the Zeno Effect<br />
| journal=[[Optical Review]]<br />
| volume=12<br />
| pages=1605-1623<br />
| year=2005<br />
}}</ref><br />
<br />
==See also==<br />
* [[Bohr model]]<br />
* [[Theoretical and experimental justification for the Schrödinger equation]]<br />
* [[Thermal de Broglie wavelength]]<br />
* [[Atomic de Broglie microscope]]<br />
<br />
==References==<br />
<references/><br />
* Steven S. Zumdahl, ''Chemical Principles 5th Edition'', (2005) Houghton Mifflin Company.<br />
*René-Louis Vallée: L'énergie électromagnétique matérielle et gravitationnelle, Paris, 1971 - translated by D.A. Borgdorff. Ibidem la SEPED - Paris, 1978 - [http://jlnlabs.online.fr/vsg/theorie/ La théorie Synergétique] {{fr}}<br />
* Tipler, Paul A. and Ralph A. Llewellyn (2003). ''Modern Physics''. 4th ed. New York; W. H. Freeman and Company. ISBN 0-7167-4345-0. pp. 203-4, 222-3, 236.<br />
* Web version of Thesis, translated (English): http://www.ensmp.fr/aflb/LDB-oeuvres/De_Broglie_Kracklauer.htm<br />
<br />
[[Category:Foundational quantum physics]]<br />
[[Category:Hypotheses]]<br />
<br />
[[bg:Вълни на дьо Бройл]]<br />
[[de:Materiewelle]]<br />
[[el:Κύματα ντε Μπρολί]]<br />
[[eu:De Broglie hipotesia]]<br />
[[es:Ondas de materia]]<br />
[[fr:Hypothèse de De Broglie]]<br />
[[he:השערת דה ברויי]]<br />
[[it:Ipotesi di de Broglie]]<br />
[[ja:ド・ブロイ波]]<br />
[[nl:Materiegolven]]<br />
[[pl:Hipoteza de Broglie'a]]<br />
[[ro:Ipoteza de Broglie]]<br />
[[fi:De Broglien aallonpituus]]<br />
[[sv:De Broglie-våglängd]]<br />
[[tr:Olasılık dalgası]]<br />
[[zh:德布羅伊假說]]<br />
<br />
{{WH}}<br />
{{WS}}</div>WikiBot