Turning the question around

Einstein had made wave-like light behave as particles. In his doctoral thesis, Louis de Broglie tried the reverse symmetry: perhaps matter normally treated as particles also has a wavelength.

λ=hp.\lambda=\frac{h}{p}.

Large momentum means a short wavelength. Everyday objects have wavelengths too small to notice, but electrons might diffract on the scale of a crystal lattice.

Matter-wave diffraction Scientific model diagram λ = h/p λ = h/p crystal, d = d crystal, d = d Crystal scattering forms discrete diffraction peaks Crystal scattering forms discrete diffraction peaks
Edit in Studio
Diagram description

Static physics diagram: de_broglie_electron_diffraction.

A thesis without direct evidence

The idea made the examiners hesitate. Paul Langevin sent the thesis to Einstein, who recognized its importance. Electron diffraction experiments soon measured wavelengths matching de Broglie’s relation.

The proposal helped Schrödinger build wave mechanics and made Bohr’s allowed states resemble standing waves that close on themselves.

De Broglie did not quietly replace particles with ordinary water waves. He showed that the classical choice between “wave” and “particle” had become too small for nature.