- De Broglie hypothesis
In
physics , the de Broglie hypothesis (pronounced /brœj/, as French breuil, close to "broy") is the statement that allmatter (any object) has awave -like nature (wave-particle duality ). The de Broglie relations show that thewavelength isinversely proportional to themomentum of a particle and that thefrequency is directly proportional to the particle'skinetic energy . The hypothesis was advanced byLouis de Broglie in 1924 in his PhD thesis [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).Reprinted in "Ann. Found. Louis de Broglie" 17 (1992) p. 22.] ; he was awarded theNobel Prize for Physics in 1929 for this work, which made him the first person to receive a Nobel Prize on a PhD thesis.Historical context
After strides made by
Max Planck (1858-1947) andAlbert 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 theRydberg equation , an equation that was discovered only through trial and error. This equation explains the energies of the 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.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 experimentally confirmed in 1927 when physicists Lester Germer and Clinton Davisson fired electrons at a crystalline nickel target and the resulting diffraction pattern was found to match the predicted values. 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 ofPlanck's constant (6.626 imes 10^{-34}joule -seconds) divided by the object's momentum (nonrelativistically, itsmass multiplied by itsvelocity ). 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 10^{-35} 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.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.The de Broglie relations
The first de Broglie equation relates the wavelength lambda to the particle momentum p~ as
:lambda = frac{h}{p} = frac {h}{gamma mv} = frac {h}{mv} sqrt{1 - frac{v^2}{c^2
where h~ is
Planck's constant , m~ is the particle'srest mass , v~ is the particle'svelocity , gamma~ is theLorentz factor , and c~ is thespeed of light in a vacuum.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:f = frac{E}{h} = frac{gamma,mc^2}{h} = frac {1}{sqrt{1 - frac{v^2}{c^2} cdot frac{mc^2}{h}
where f~ is the frequency and E~ is the total energy. The two equations are often written as
:p = hbar k:E = hbar omega
where p~ is momentum, hbar=h/(2pi)~ is the reduced
Planck's constant (also known as Dirac's constant, pronounced "h-bar"), k~ is the wavenumber, and omega~ is theangular frequency .See the article on
group velocity for detail on the argument and derivation of the de Broglie relations.Experimental confirmation
Elementary particles
In 1927 at Bell Labs,
Clinton Davisson andLester Germer fired slow-movingelectrons at acrystalline nickel target. The angular dependence of the reflected electron intensity was measured, and was determined to have the same diffraction pattern as those predicted by Bragg for 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 anydiffraction effects by matter demonstrated the wave-like nature of matter. When the de Broglie wavelength was inserted into the Bragg condition, the observed diffraction pattern was predicted, thereby experimentally confirming the de Broglie hypothesis for electrons.This was a pivotal result in the development of
quantum mechanics . Just asArthur Compton demonstrated the particle nature of light, theDavisson-Germer experiment showed the wave-nature of matter, and completed the theory of wave-particle duality. Forphysicists this idea was important because it means that not only can any particle exhibit wave characteristics, but that one can usewave equation s to describe phenomena in matter if one uses the de Broglie wavelength.Since the original Davisson-Germer experiment for electrons, the de Broglie hypothesis has been confirmed for other
elementary particles .Neutral atoms
Experiments with
Fresnel diffraction cite journal| url=http://prola.aps.org/abstract/PRL/v83/i21/p4229_1
author=R.B.Doak | coauthors=R.E.Grisenti, S.Rehbein, G.Schmahl, J.P.Toennies2, and Ch. Wöll
title=Towards Realization of an Atomic de Broglie Microscope: Helium Atom Focusing Using Fresnel Zone Plates
journal=PRL | volume=83 | pages=4229–4232 | year=1999
doi=10.1103/PhysRevLett.83.4229 ] andspecular reflection cite journal | url=http://prola.aps.org/abstract/PRL/v86/i6/p987_1
author= F. Shimizu | title=Specular Reflection of Very Slow Metastable Neon Atoms from a Solid Surface
journal=PRL| volume=86| pages=987–990 | year=2000 | doi=10.1103/PhysRevLett.86.987] cite journal
comment=7
url=http://annex.jsap.or.jp/OSJ/opticalreview/TOC-Lists/vol12/12e0363tx.htm
author= D. Kouznetsov
coauthors= H. Oberst
title=Reflection of Waves from a Ridged Surface and the Zeno Effect
journal=Optical Review
volume=12
pages=1605–1623
year=2005
doi=10.1007/s10043-005-0363-9] of neutral atomsconfirm the application of the De Broglie hypothesis to atoms, i.e. the existence of atomic waves which undergodiffraction ,interference and allowquantum reflection by the tails of the attractive potentialcite journal
author=H.Friedrich
coauthors=G.Jacoby, C.G.Meister
journal=PRA
title=quantum reflection by Casimir–van der Waals potential tails
year=2002
volume=65
url=http://prola.aps.org/abstract/PRA/v65/i3/e032902
pages=032902
doi=10.1103/PhysRevA.65.032902] .This effect has been used to demonstrate atomicholography , and it may allow the construction of an atom probe imaging system with nanometer resolution.cite journal |title=Reflection-Type Hologram for Atoms |author=Shimizu |coauthors=J.Fujita |journal=Physical Review Letters |volume=88 |number=12 |pages=123201 |year=2002 |url=http://prola.aps.org/abstract/PRL/v88/i12/e123201 |doi=10.1103/PhysRevLett.88.123201 |publisher=American Physical Society ] cite journal |url=http://stacks.iop.org/0953-4075/39/1605 |author=D. Kouznetsov |coauthors=H. Oberst, K. Shimizu, A. Neumann, Y. Kuznetsova, J.-F. Bisson, K. Ueda, S. R. J. Brueck |title=Ridged atomic mirrors and atomic nanoscope |journal=Journal of Physics B |volume=39 |pages=1605–1623 |year=2006 |doi=10.1088/0953-4075/39/7/005] The description of these phenomena is based on the wave properties of neutral atoms, confirming the de Broglie hypothesis.Waves of molecules
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 inVienna demonstrated diffraction for molecules as large asfullerenes [cite journal| title=Wave-particle duality of C60| first=M.| last=Arndt| coauthors=O. Nairz, J. Voss-Andreae, C. Keller, G. van der Zouw, A. Zeilinger| journal=Nature| volume=401| pages=680–682| month=14 October| year=1999| doi=10.1038/44348] .In general, the De Broglie hypothesis is expected to apply to any well isolated object.
patial Zeno effect
The De Broglie hypothesis leads to the spatial version of the
Zeno effect . If an object (particle) is observed with frequency Omegaggomega~in a half-space (say, y<0~), then this observation prevents the particle, which stays in the half-space y>0~ from entry into this half-space y<0~. 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 the ridges, this phenomenon appears as aspecular reflection of a particle from aridged mirror , assuming the grazing incidence (small values of thegrazing angle ).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 k~ and does not depend on other properties of a particle.cite journal
comment=7
url=http://annex.jsap.or.jp/OSJ/opticalreview/TOC-Lists/vol12/12e0363tx.htm
author= D.Kouznetsov
coauthors= H.Oberst
title=Reflection of Waves from a Ridged Surface and the Zeno Effect
journal=Optical Review
volume=12
pages=1605–1623
year=2005
doi=10.1007/s10043-005-0363-9]ee also
*
Bohr model
*Theoretical and experimental justification for the Schrödinger equation
*Thermal de Broglie wavelength
*Atomic de Broglie microscope References
* Steven S. Zumdahl, "Chemical Principles 5th Edition", (2005) Houghton Mifflin Company.
* [http://www.nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-lecture.pdf Broglie, Louis de, The wave nature of the electron, Nobel Lecture, 12, 1929]
* Tipler, Paul A. and Ralph A. Llewellyn (2003). "Modern Physics". 4th ed. New York; W. H. Freeman and Co. ISBN 0-7167-4345-0. pp. 203-4, 222-3, 236.
* Web version of Thesis, translated (English): http://www.ensmp.fr/aflb/LDB-oeuvres/De_Broglie_Kracklauer.htm
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