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Albert Einstein correctly described the photoelectric effect by suggesting that electrons had certain discrete energy levels, and that light was composed of particles which carried certain discrete energies. He showed that the energy that these light particles (photons) carried was proportional to the frequency of the light. So for certain frequencies of light, electrons in a material could absorb the photons and gain the energy needed to leave the material. Albert Einstein discovered the quantum of light.

Louis de Broglie then suggested that if light (a wave) could also be described by photons (particles), then perhaps electrons (particles) could be described as waves. A series of experiments showed that de Broglie's theory was correct.

Erwin Schrödinger later discovered an equation which correctly modeled the wave nature of matter.

Many textbooks attribute the discovery of quantum mechanics to Max Planck, and he won the 1918 Nobel prize for "the discovery of energy quanta," but neither he nor the vast majority of the scientific community at the time (at the time of his 1900 discovery of the Planck radiation law, that is) recognized that his use of energy quanta in describing black body radiation suggested a new hypothesis that would be later known as quantum theory (see Kragh, Helge. "Max Planck: The Reluctant Revolutionary." Physics World. December 2000)

In short, the discovery of quantum mechanics was an extended process which could not have been made possible if it were not for several physicists.

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