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Matter wave, which is also referred to as de Broglie wave, explains how massive particles behave like waves. For example, a beam of electrons can be diffracted just like a beam of light or a water wave.
The de Broglie hypothesis showed that wave-particle duality was not merely an aberrant behavior of light, but rather was a fundamental principle exhibited by both radiation and matter. As such, it becomes possible to use wave equations to describe material behavior, so long as one properly applies the de Broglie wavelength. This would prove crucial to the development of quantum mechanics. It is now an integral part of the theory of atomic structure and particle physics.
By the early 1920s, the photon theory of light was well established. However, physicists were still struggling with how to describe particles such as electrons in the quantum world.
In his 1924 Ph.D. thesis, Louis de Broglie first suggested that all matter have wave-like properties. This hypothesis forms a central part of the theory of quantum mechanics, and he received the 1929 Nobel Prize for his theory (the first time it was ever awarded for a Ph.D. thesis).
(15 August 1892 – 19 March 1987)
At the time when he publish his thesis, experimental evidence of interference with electrons had not yet been discovered.
It was not until 1927, that de Broglie's hypothesis was confirmed with the observation of electron diffraction in two independent experiments. At the Bell Labs, two American physicists Clinton Davisson and Lester Germer fired slow moving electrons at a crystalline nickel target, and the result was determined to have the same diffraction pattern as de Broglie hypothesized. Around the same time at the University of Aberdeen, George Paget Thomson passed a beam of electrons through a thin metal film and observed the predicted interference patterns. De Broglie received the 1929 Nobel Prize after his hypothesis has been experimentally confirmed.
Davisson–Germer experiment
Book
Bruni, D., & DiGiuseppe, M. (2012). Nelson Physics 12: university preparation. Scarborough, Ont.: Thomson/Nelson.
Websites
L. (2016, July 21). Wave-Particle Duality. Retrieved September 08, 2017, from https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Quantum_Mechanics/09._The_Hydrogen_Atom/Atomic_Theory/Electrons_in_Atoms/Wave-Particle_Duality
Louis de Broglie - Nobel Lecture. (n.d.). Retrieved September 08, 2017, from https://www.nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-lecture.html
Jones, A. Z. (n.d.). What Is the De Broglie Hypothesis? Retrieved September 08, 2017, from https://www.thoughtco.com/de-broglie-hypothesis-2699351
The Wave Structure of Matter (WSM) and Spherical Standing Wave. (n.d.). Retrieved September 08, 2017, from http://www.spaceandmotion.com/Physics-Louis-de-Broglie.htm
Lousi de Broglie. (n.d.). Retrieved September 08, 2017, from https://micro.magnet.fsu.edu/optics/timeline/people/debroglie.html
"The fundamental idea of [my 1924 thesis] was the following: The fact that, following Einstein's introduction of photons in light waves, one knew that light contains particles which are concentrations of energy incorporated into the wave, suggests that all particles, like the electron, must be transported by a wave into which it is incorporated... My essential idea was to extend to all particles the coexistence of waves and particles discovered by Einstein in 1905 in the case of light and photons." "With every particle of matter with mass m and velocity v a real wave must be 'associated'", related to the momentum by the equation:
where λ is the wavelength, h is the Planck constant, p is the momentum, m is the rest mass, v is the velocity.
de Broglie wavelength: the wavelength associated with the motion of a particle possessing momentum of magnitude p