According to de Broglie, a particle of mass m moving with a speed v should, under suitable experimental conditions, exhibit the characteristics of a wave of wavelength
λ = \(\cfrac h{mv}\) = \(\cfrac hp\).......(1)
where p = mv ≡ momentum of the particle and h is Planck’s constant.
This dual character of matter contained in Eq. (1) is usually referred to as the wave nature of matter or matter waves. They are a set of waves that represent the behaviour of particles under appropriate conditions. It does not, however, mean that the particles themselves are oscillating in space.
Interpretation of matter waves by Max Born (1882-1970), German bom British physicist, is that they are waves of probability, since the square of their amplitude at a given point is linked to the likelihood of finding the particle there. Hence, the wavelength λ may be regarded as a measure of the degree to which the energy is localized. If λ is exceedingly small, the energy is very localized and the particle character of the object is dominant. On the other hand, if λ is very large, the energy is distributed over a large volume; under these circumstances, the wave behaviour is dominant.
The wave nature of material particles such as the electron, neutron and helium atom has been established experimentally beyond doubt.
