The Planck relation[1][2][3] (referred to as Planck's energyâfrequency relation,[4] the PlanckâEinstein relation,[5]Planck equation,[6] and Planck formula,[7] though the latter might also refer to
Planck's law[8][9]) is a fundamental equation in
quantum mechanics which states that the energy E of a
photon, known as
photon energy, is proportional to its
frequencyν:
The
constant of proportionality, h, is known as the
Planck constant. Several equivalent forms of the relation exist, including in terms of
angular frequencyĎ:
where . Written using the symbol f for frequency, the relation is
The de Broglie relation,[10][11][12] also known as de Broglie's momentumâwavelength relation,[4] 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 Îť = h/p. Combining de Broglie's postulate with the PlanckâEinstein relation leads to
or
The de Broglie relation is also often encountered in
vector form
where p is the momentum vector, and k is the
angular wave vector.
Bohr's frequency condition
Bohr's frequency condition[13] states that the frequency of a photon absorbed or emitted during an
electronic transition is related to the energy difference (ÎE) between the two
energy levels involved in the transition:[14]
This is a direct consequence of the PlanckâEinstein relation.
Cohen-Tannoudji, C., Diu, B., LaloĂŤ, 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.
van der Waerden, B.L. (1967). Sources of Quantum Mechanics, edited with a historical introduction by B.L. van der Waerden, North-Holland Publishing, Amsterdam.
Weinberg, S. (1995). The Quantum Theory of Fields, volume 1, Foundations, Cambridge University Press, Cambridge UK,
ISBN978-0-521-55001-7.