The Dawn Of The Prince Of Quantum Physics
De Broglie Hypothesis
De Broglie Hypothesis also was popularly known as the matter waves which states that “all matter exhibits wavelike properties. Such that a beam of electrons can be diffracted just as a beam of light or a water wave.
Demonstration of a matterwave in the diffraction of electrons. Credit: Wikipedia 
De Broglie, in his 1924 Ph.D. papers, introduced a concept same as light having both particlelike and wavelike properties, similarly electrons (in fact all the matter) also have wavelike properties too. According to the assumptions made by Louis De Broglie, if a light has both particles as well as wave nature then this may be also true for all types of matter also.
Albert Einstein was the first one to explain the waveparticle duality of light in his photoelectric effect theory. De Broglie hypothesized that any particle should also exhibit such duality and as a byproduct of waveparticle duality, De Broglie further conceptualized the standing wave to be related to discrete wavelength. And as a result, the wave nature of a particle is quantified by de Broglie hypothesis.
Artistic representation of waveparticle duality. CREDIT: quantumlah.org 
In De Broglie’s view, the sum of the total energy of this vast universe can only be explained in the form of radiation and matter. Therefore, both radiation and matter should have similar properties. So, radiation shows dual nature ( Planck’s Hypothesis For BlackBody Radiation), similarly matter also should have wave properties too which can be expressed as:
where,
h = Planck’s Constant
p = momentum of a particle
λ = de Broglie wavelength
In the above equation, De Broglie concluded the two observed phenomena (Planck’s Quantum theory and Einstein’s special relativity) with mathematical certainty.
Thus for the first time in the history of the scientific timeline uniting these two theories by one common theoretical foundation.
✱ above relationship correctly stands for all types of matter.
When I conceived the first basic ideas of wave mechanics in 1923–24, I was guided by the aim to perform a real physical synthesis, valid for all particles, of the coexistence of the wave and of the corpuscular aspects that Einstein had introduced for photons in his theory of light quanta in 1905.
λpλ=h
Criticism And Support
Well according to Louis Victor De Broglie, not just light– our whole world is quantum. A conclusion so bold that as a result it was immediately rejected by many pioneers of the scientific world such as Wolfgang Pauli etc. But that was not the case with Albert Einstein who warmly supported the De Broglie conclusion.
As Einstein states (in 1954)
Experiments on interference made with particle ray have given brilliant proof that the wave character phenomena of motion as assumed by the theory does, really corresponds to the facts
✱ Even Einstein’s support was not enough to prove the de Broglie’s hypothesis right. De Broglie’s hypothesis had to be experimentally demonstrated.
Experimental Confirmation
De Broglie waves or matter waves or wavelike behavior of matter was first experimentally demonstrated by George Paget Thomson’s (Son Of J.J Thomson) thin metal diffraction experiment. Later in 1927, the matterwave was independently confirmed by American physicists Clinton Davisson and Lester Germer in their experimental demonstration named DavissonGermer experiment. All three of them ( George Paget Thomson, Clinton Davisson, and Lester Germer) shared the noble prize for physics in 1937 for their independent demonstration of the matter waves or de Broglie waves.
Experimental Setup for DavissonGermer Experiment CREDIT: Wikipedia 
Later it was also confirmed for other elementary particles, atoms, even some molecules too. The De Broglie Hypothesis for matterwave is very crucial to atomic physics as well as particle physics. The confirmation of waveparticle duality was an important historical development for the establishment of quantum mechanics and the Schrodinger equation.
Therefore, by uniting the physics of energy (wave) and matter (particle), Louis Victor de Broglie invented a new field of physics which is today known to us as wave mechanics
Thus finally confirming the De Broglie hypothesis for matterwave, who was later awarded the Nobel prize for physics in 1929 just after five years he had presented his doctoral thesis.
Determination of the stable motion of electrons in the atom introduces integers, and up to this point the only phenomena involving integers in physics were those of interference and of normal modes of vibration. This fact suggested to me the idea that electrons too could not be considered simply as particle, but that frequency (wave properties) must be assigned to them also.
(Louis de Broglie, on Quantum Theory, 1929, Nobel Prize Speech)
✱ Electron Microscope is an application of the De Broglie Hypothesis.
Pollen grains image taken on an electron microscope, an application of the De Broglie Hypothesis. Credit: bodyquirks.com

The electron can no longer be conceived as a single, small granule of electricity; it must be associated with a wave, and this wave is no myth; its wavelength can be measured and its interferences predicted.
Louis Victor De Broglie