Planck-Einstein relation

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The Planck-Einstein relation is the formula

E\,=\,h\nu\,=\,\hbar \omega,


E is the energy of a photon
ν the photon's frequency
ω the photon's angular frequency
h is Planck's constant
ħ reduced Planck's constant, where ħ = h/2π.[1][2]

The formula is also referred to as the Einstein relation,[1][3][4] and as Planck's energy–frequency relation,[5] and as the Planck relation.[6]

Alternative usages[edit]

The term Planck–Einstein relation also can refer to the closely related formula

\mathbf p\,=\,\hbar \mathbf k\,,

where p denotes the momentum of the photon and k its angular wavenumber.[2]

The term Einstein relation can also refer to the formula


where E denotes the energy of a particle and m its mass; c denotes the speed of light.[7]

Related formula[edit]

The formula E = is related to Bohr's frequency condition


where E and E′′ denote the source and destination energy levels of an atom that emits the photon.[8]


  1. ^ a b French, A.P., Taylor, E.F. (1978), pp. 24, 55.
  2. ^ a b Cohen-Tannoudji, C., Diu, B., Laloë, F. (1973/1977), pp. 10–11.
  3. ^ Messiah, A. (1958/1961), p. 72.
  4. ^ Weinberg, S. (1995), p. 3.
  5. ^ Schwinger, J. (2001), p. 203.
  6. ^ Landsberg, P.T. (1978), p. 199.
  7. ^ Schwinger, J. (2001), p. 22.
  8. ^ van der Waerden, B.L. (1967), p. 5.

Cited bibliography[edit]