French physicist Louis de Broglie proposed this hypothesis. It was a ground breaking hypothesis in fact. Earlier Louis de Broglie was a student of history, later he built his career in physics. He proposed this famous theory in his PhD thesis in 1924 (some people think the year was 1923).

Newton thought light consists of tiny particles. But wave theory was adopted to explain some optical phenomena like interference and diffraction. In 1905 Albert Einstein considered light as stream of particles to explain photoelectric effect.

Louis de Broglie extended this property to every particle including electron, proton, neutron, atom and molecule. This theory is even applicable for matter. He proposed, wave is associated to every moving particles and matter. According to de Broglie hypothesis electron is not only particle, it also have wave property. Later his hypothesis was verified experimentally by Davisson and Germer.

According to Plank-Einstein equation, for any electromagnetic wave,

Where E is the energy of photon, h is plank’s constant and n is frequency of electromagnetic wave.

From theory of relativity,

Where p is relativistic momentum and m_{0} is rest mass.

Rest mass of photon is zero, so above equation can be written as,

From equation (1) and (3),

or,

or,

So if we run, we have an associated de Broglie wave too! Now question is, why we do not notice this wave?

The answer is in the equation no. 4. As momentum is dependent on speed and mass, larger objects like us or football has larger momentum. Plank’s constant h is so small (6.6256×10^{-34}Js) and when this constant is divided by a large momentum its wavelength becomes impossible to notice. But electron or electron like particles has very small momentum and they exhibit demonstrable wave properties.