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Energy-frequency relation in quantum mechanics
The Planck–Einstein relation is also referred to as the Einstein relation,Planck's energy–frequency relation, the Planck relation, and the Planck equation. Also the eponym Planck formula belongs on this list, but also often refers to Planck's law instead. These various eponyms are far from standard; they are used only sporadically, neither regularly nor very widely. They refer to a formula integral to quantum mechanics, which states that the energy of a photon, E, known as photon energy, is proportional to its frequency, ν:
The de Broglie relation, also known as the de Broglie's momentum–wavelength relation, generalizes the Planck relation to matter waves. Louis de Broglie argued that if particles had a wave nature, the relation E = hν would also apply to them, and postulated that particles would have a wavelength equal to λ = h/p. Combining de Broglie's postulate with the Planck–Einstein relation leads to
The de Broglie's relation is also often encountered in vector form
Cohen-Tannoudji, C., Diu, B., Laloë, F. (1973/1977). Quantum Mechanics, translated from the French by S.R. Hemley, N. Ostrowsky, D. Ostrowsky, second edition, volume 1, Wiley, New York, ISBN0471164321.