Do you know who this equation is named after?
At the end of the 19th century, light was thought to consist of waves of electromagnetic fields which propagated according to Maxwell’s equations, while matter was thought to consist of localized particles (See history of wave and particle viewpoints). In 1900, this division was exposed to doubt, when, investigating the theory of black body thermal radiation, Max Planck proposed that light is emitted in discrete quanta of energy. It was thoroughly challenged in 1905. Extending Planck’s investigation in several ways, including its connection with the photoelectric effect, Albert Einstein proposed that light is also propagated and absorbed in quanta. Light quanta are now called photons. These quanta would have an energy given by the Planck–Einstein relation:
and a momentum
where ν and λ denote the frequency and wavelength of the light, c the speed of light, and h the Planck constant.
De Broglie, in his 1924 PhD thesis, proposed that just as light has both wave-like and particle-like properties, electrons also have wave-like properties. By rearranging the momentum equation stated above, we find a relationship between the wavelength, λ associated with an electron and its momentum, p, through the Planck constant, h:
The relationship is now known to hold for all types of matter: all matter exhibits properties of both particles and waves.