### De Broglie's Thesis

In his 1923 (or 1924, depending on the source) doctoral dissertation, the French physicist Louis de Broglie made a bold assertion. Considering Einstein's relationship of wavelength*lambda*to momentum

*p*, de Broglie proposed that this relationship would determine the wavelength of any matter, in the relationship:

This wavelength is called thelambda=h/precall that

his Planck's constant

*de Broglie wavelength*. The reason he chose the momentum equation over the energy equation is that it was unclear, with matter, whether

*E*should be total energy, kinetic energy, or total relativistic energy. For photons they are all the same, but not so for matter.

Assuming the momentum relationship, however, allowed the derivation of a similar de Broglie relationship for frequency *f* using the kinetic energy *E _{k}*:

f=E/_{k}h

### Alternate Formulations

De Broglie's relationships are sometimes expressed in terms of Dirac's constant,*h-bar*=

*h*/ (2

*pi*), and the angular frequency

*w*and wavenumber

*k*:

p=h-bar*k

E=_{k}h-bar*w

### Experimental Confirmation

In 1927, physicists Clinton Davisson and Lester Germer, of Bell Labs, performed an experiment where they fired electrons at a crystalline nickel target. The resulting diffraction pattern matched the predictions of the de Broglie wavelength. De Broglie received the 1929 Nobel Prize for his theory (the first time it was ever awarded for a Ph.D. thesis) and Davisson/Germer jointly won it in 1937 for the experimental discovery of electron diffraction (and thus the proving of de Broglie's hypothesis).Further experiments have held de Broglie's hypothesis to be true, including the quantum variants of the double slit experiment. Diffraction experiments in 1999 confirmed the de Broglie wavelength for the behavior of molecules as large as buckeyballs (complex molecules made up of 60 or more carbon atoms).