**Quantum Mechanics and Momentum**

Part 1: The De Broglie Relations

Planck’s relation tells us that the energy of a photon is proportional to the frequency: *E*=*hν*, where *h* is Planck’s constant. In terms of angular frequency *ω*, we use *ω*=2π*ν* to find that , where is called the reduced Planck constant, or the Dirac constant.

Classical electrodynamics of an electromagnetic wave and the relativistic energy-momentum relation for a particle with zero rest mass both give the same result for the momentum of a photon: that , and so the momentum is

, where *λ* is the wavelength. Solving for wavelength, we have . This wavelength can be found for any particle, not just photons, and is called the de Broglie wavelength (see here for details on the historical context and experimental support for this).

Now, let us consider the corresponding angular wavenumber . Then we have

or .

The two equations, and , are known as the de Broglie relations, and the latter one will be important in the later parts of this series.

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Tags: de Broglie, Energy, Friday Physics, Momentum, physics, Quantum Mechanics, Wavelength, Wavenumber

This entry was posted on October 31, 2008 at 12:01 am and is filed under Math/Science. You can follow any responses to this entry through the RSS 2.0 feed.
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November 14, 2008 at 12:09 am |

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