## Particlewave Nature of Light and Matter DeBroglie Formulas A hp E hv

One of the most direct indications of the wave nature of light is the sinusoidal interference pattern of coherent light falling on a screen behind two linear slits of small spacing, d. The rule for appearance of maxima at angular position 0 in the interference pattern, nA= dsin0, (4.5)

is that the difference in the path length of the light from the two slits shall be an integral number n of light wavelengths, nX. Dark regions in the interference pattern occur at locations where the light waves from the two slits arrive 180 degrees out of phase, so that they exactly cancel.

The first prediction of a wave nature of matter was given by Louis DeBroglie [3]. This young physics student postulated that since light, historically considered to be wavelike, was established to have a particle nature, it might be that matter, considered to be made of particles, might have a wave nature. The appropriate wavelength for matter, DeBroglie suggested, is

where h is Planck's constant, and p = mv is the momentum. For light p = E/c, so the relation X=hjp can be read as A= hc/E = c/v. Filling out his vision of the symmetry between light and matter, DeBroglie also said that the frequency v associated with matter is given by the same relation,

as had been established for light by Planck.

This postulated wave property of matter was confirmed by observation of electron diffraction by Davisson and Germer [4]. The details of the observed diffraction pat-

4.3 Wavefunction Wfor Electron, Probability Density W*W, Traveling and Standing Waves terns could be fitted if the wavelength of the electrons was exactly given by h/p. For a classical particle, A= h/(2mE)1^2, since p2 = 2mE. So there was no doubt that a wave nature for matter particles is correct, as suggested by DeBroglie [3]. The question then became one of finding an equation to determine the wave properties in a given situation.

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