Planck–Einstein relation

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The Planck–Einstein relation[1][2] is also referred to as the Einstein relation,[1][3][4] Planck's energy–frequency relation,[5] the Planck relation,[6] and the Planck equation.[7] Also the eponym 'Planck formula'[8] belongs on this list, but also often refers instead to Planck's law[9][10] 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) is proportional to its frequency (ν).

E = h \nu


The relation accounts for quantized nature of light, and plays a key role in understanding phenomena such as the photoelectric effect, and Planck's law of black body radiation. See also the Planck postulate.

Spectral forms[edit]



so the Planck relation can take the following 'standard' forms


as well as the following 'angular' forms,



de Broglie relation[edit]


p = h \tilde \nu or
p = \hbar k.

The de Broglie's relation is also often encountered in vector form



Bohr's frequency condition[edit]


\Delta E = h \nu.

This is a direct consequence of the Planck–Einstein relation.


  6. ^ Landsberg (1978), p. 199.
  7. ^ Landé (1951), p. 12.
  8. ^ Griffiths, D.J. (1995), pp. 143, 216.
  9. ^ Griffiths, D.J. (1995), pp. 217, 312.
  10. ^ Weinberg (2013), pp. 24, 28, 31.
  11. ^ Messiah (1958/1961), p. 14.
  13. ^ van der Waerden (1967), p. 5.

Cited bibliography[edit]