De Broglie Waves
In physics, the matter wave, aka de Broglie wave, 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 wavelength of matter is also called de Broglie wavelength. The theory was advanced by Louis de Broglie in 1924 in his PhD thesis; 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.
Historical context[edit]
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 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. 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 (6.626×10−34 joule-seconds) divided by the object's 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 10−35 meter 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.
