Question

The relationship between waves and matter ?

Answer 1

After all experimental evidences, first of all photoelectric effect presented by Einstein, in 1924 Louise De Broglie intended to express a synthesis of several precedent hypothesis about a relation between the coexistent nature of wave and matter in a elementary particles. He wrote `lambda=h/p` that links a wave propriety (`lambda`) with a matter property (p=m*v) by the Plank constant h.

Explanation:

The written formula is a quantistic quantitative interpretation of wave-matter duality and gives an estimate of the wavelength `lambda` associated to a particle of linear momentum p. On the other hand, previously was established the waves quantization introducing the particle interpretation of radiation by the photon.
The formula works well for the most simple experimental verifications, but generalization of duality is still a discussed and opened question relatively the more complex systems than a particle. The further step to interpretation of duality, was given by Werner Heisenberg with his uncertainty principle that
pointed out and related the weak localization of a particle as so that wave one.