Planck relation

Light can be characterized using several spectral quantities, such as frequency , wavelength , wavenumber \tilde{\nu}, and their angular equivalents (angular frequency , angular wavelength , and angular wavenumber ). These quantities are related through \nu = \frac{c}{\lambda} = c \tilde \nu = \frac{\omega}{2 \pi} = \frac{c}{2 \pi y} = \frac{ck}{2 \pi}, so the Planck relation can take the following "standard" forms: E = h \nu = \frac{hc}{\lambda} = h c \tilde \nu, as well as the following "angular" forms: E = \hbar \omega = \frac{\hbar c}{y} = \hbar c k. The standard forms make use of the Planck constant . The angular forms make use of the reduced Planck constant . Here is the speed of light. ==de Broglie relation==

The de Broglie relation, also known as 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 would also apply to them, and postulated that particles would have a wavelength equal to . Combining de Broglie's postulate with the Planck–Einstein relation leads to p = h \tilde \nu or p = \hbar k. The de Broglie relation is also often encountered in vector form \mathbf{p} = \hbar \mathbf{k}, where is the momentum vector, and is the angular wave vector. ==Bohr's frequency condition==

Bohr's frequency condition states that the frequency of a photon absorbed or emitted during an electronic transition is related to the energy difference () between the two energy levels involved in the transition: \Delta E = h \nu. This is a direct consequence of the Planck–Einstein relation. ==See also==

• 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, . • French, A.P., Taylor, E.F. (1978). An Introduction to Quantum Physics, Van Nostrand Reinhold, London, . • Griffiths, D.J. (1995). Introduction to Quantum Mechanics, Prentice Hall, Upper Saddle River NJ, . • Landé, A. (1951). Quantum Mechanics, Sir Isaac Pitman & Sons, London. • Landsberg, P.T. (1978). Thermodynamics and Statistical Mechanics, Oxford University Press, Oxford UK, . • Messiah, A. (1958/1961). Quantum Mechanics, volume 1, translated from the French by G.M. Temmer, North-Holland, Amsterdam. • Schwinger, J. (2001). Quantum Mechanics: Symbolism of Atomic Measurements, edited by B.-G. Englert, Springer, Berlin, . • 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, . • Weinberg, S. (2013). Lectures on Quantum Mechanics, Cambridge University Press, Cambridge UK, .