In physics, the de Broglie hypothesis 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^[1]; 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. Physics (Greek: (phúsis), nature and (phusiké), knowledge of nature) is the branch of science concerned with the fundamental laws of the Universe. ... This article or section does not cite any references or sources. ... This article is about waves in the most general scientific sense. ... In physics, wave-particle duality holds that light and matter exhibit properties of both waves and of particles. ... The wavelength is the distance between repeating units of a wave pattern. ... This article is about proportionality, the mathematical relation. ... In classical mechanics, momentum (pl. ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ... The kinetic energy of an object is the extra energy which it possesses due to its motion. ... Louis-Victor-Pierre-Raymond, 7th duc de Broglie, generally known as Louis de Broglie (August 15, 1892–March 19, 1987), was a French physicist and Nobel Prize laureate. ... 1924 (MCMXXIV) was a leap year starting on Tuesday (link will display the full calendar). ... List of Nobel Prize laureates in Physics from 1901 to the present day. ... 1929 (MCMXXIX) was a common year starting on Tuesday (link will take you to calendar). ...

The de Broglie relations

The first de Broglie equation relates the wavelength to the particle momentum as

where λ is the particle's wavelength, h is Planck's constant, p is the particle's momentum, m is the particle's rest mass, v is the particle's velocity, γ is the Lorentz factor, and c is the speed of light in a vacuum. The wavelength is the distance between repeating units of a wave pattern. ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... In classical mechanics, momentum (pl. ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ... This article or section does not cite its references or sources. ... It has been suggested that Lorentz term be merged into this article or section. ... A line showing the speed of light on a scale model of Earth and the Moon The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation...

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 a particle to the kinetic energy such that FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ...

where f is the frequency and E_k is the kinetic energy. The two equations are often written as

where is the reduced Planck's constant, pronounced "h-bar," k is the wavenumber, and ω is the angular frequency. A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... Wavenumber in most physical sciences is a wave property inversely related to wavelength, having SI units of reciprocal meters (m−1). ... It has been suggested that this article or section be merged into Angular velocity. ...

See the article on group velocity for detail on the argument and derivation of the de Broglie relations. The group velocity of a wave is the velocity with which the variations in the shape of the waves amplitude (known as the modulation or envelope of the wave) propagate through space. ...

Experimental confirmation

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 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 any diffraction 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. Clinton Joseph Davisson (22 October 1881–1 February 1958), was an American physicist. ... Lester Germer (full name Lester Halbert Germer; 1896–1971), American physicist. ... Properties The electron (also called negatron, commonly represented as e−) is a subatomic particle. ... Crystal (disambiguation) Insulin crystals A crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions. ... General Name, Symbol, Number nickel, Ni, 28 Chemical series transition metals Group, Period, Block 10, 4, d Appearance lustrous, metallic and silvery with a gold tinge Standard atomic weight 58. ... The intensity pattern formed on a screen by diffraction from a square aperture Diffraction refers to various phenomena associated with wave propagation, such as the bending, spreading and interference of waves passing by an object or aperture that disrupts the wave. ... Sir William Lawrence Bragg CH, FRS, (31 March 1890 – 1 July 1971) was an Australian physicist who shared the Nobel Prize in Physics in 1915 with his father Sir William Henry Bragg. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... The intensity pattern formed on a screen by diffraction from a square aperture Diffraction refers to various phenomena associated with wave propagation, such as the bending, spreading and interference of waves passing by an object or aperture that disrupts the wave. ... In physics, Braggs law is the result of experiments into the diffraction of X-rays or neutrons off crystal surfaces at certain angles, derived by physicists Sir W.H. Bragg and his son Sir W.L. Bragg in 1912, and first presented on 1912-11-11 to the Cambridge...

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 equations to describe phenomena in matter if one uses the de Broglie wavelength. Fig. ... Arthur Holly Compton (September 10, 1892 – March 15, 1962) won the Nobel Prize in Physics (1927) for discovery of the Compton effect named in his honor. ... In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline Nickel target. ... Many famous physicists of the 20th and 21st century are found on the list of recipients of the Nobel Prize in physics. ... The wave equation is an important partial differential equation that describes the propagation of a variety of waves, such as sound waves, light waves and water waves. ...

Since the original Davisson-Germer experiment for electrons, the de Broglie hypothesis has been confirmed for other elementary particles. Recent experiments even confirm the relations for 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.^[2] In particle physics, an elementary particle is a particle of which other, larger particles are composed. ... A macromolecule is a molecule composed of a very large number of atoms. ... 1999 (MCMXCIX) was a common year starting on Friday, and was designated the International Year of Older Persons by the United Nations. ... Vienna (German: , see also other names) is the capital of Austria, and also one of the nine States of Austria. ... Buckminsterfullerene (C60) Fullerenes are molecules composed entirely of carbon, taking the form of a hollow sphere, ellipsoid, or tube. ...

See also

• Bohr model
• Theoretical and experimental justification for the Schrödinger equation
• Thermal de Broglie wavelength

The Bohr model of the hydrogen atom, where negatively charged electrons confined to atomic shells encircle a small positively charged atomic nucleus, and that an electron jump between orbits must be accompanied by an emitted or absorbed amount of electromagnetic energy hν. The orbits that the electrons travel in are... The theoretical and experimental justification for the Schrödinger equation motivates the discovery of the Schrödinger equation, the equation that describes the dynamics of nonrelativistic particles. ... In physics, the Thermal de Broglie wavelength is defined for a free ideal gas of massive particles in equilibrium as: where h is Plancks constant m is the mass of a gas particle k is Boltzmanns constant T is the Temperature of the gas The thermal de Broglie...

References

1. ^ 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.
2. ^ Arndt, M.; O. Nairz, J. Voss-Andreae, C. Keller, G. van der Zouw, A. Zeilinger (14 October 1999). "Wave-particle duality of C60". Nature 401: 680-682. 

• Steven S. Zumdahl, Chemical Principles 5th Edition, (2005) Houghton Mifflin Company.
• 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.
• Web version of Thesis, translated (English): http://www.ensmp.fr/aflb/LDB-oeuvres/De_Broglie_Kracklauer.htm