Please Discribe Matter Waves

Nature abounds in symmetries of all kinds. If light can be both wave and particle, is it possible that matter can also have these two aspects? Can the electron, traditionally regarded as a particle since its discovery in 1898, also have a wave aspect? More specifically, can we assign a wavelength and a frequency to a moving electron?

In 1924, the French physicist Prince Louis-Vector de Broglie (1892-1987), motivated entirely by this symmetry argument, answered yes to these questions. He proposed that an electron of energy E and linear momentum p can be described by a matter wave whose wavelength and frequency are given by

λ = h/p

and f =E/h

in which h is the Planck constant. Note that thee equations are exactly the same as those that we used to describe the photon. Except that here we have solved them for λ and f instead of for p and E. the wavelength of a moving particle calculation is called its de Broglie wavelength. De Broglie shared the 1929 Nobel Prize for his discovery of the wave nature of matter.

Objects such as marbles or baseballs do not seem at all wave-like to us. We can understand why this is so because the Planck constant h is so small and the momentum p of even slowly moving macroscopic objects is so large that the calculated de Broglie wavelengths of such objects are small indeed, being many orders of magnitude smaller than the size of atomic nucleus. It seems impossible to design an experiment to reveal the wave nature of such large scale objects. In the nest section we will see that this wave like behavior is quite common for electrons and other microscopic particles.