It is not exactly quantum mechanics; it's a classical-mechanical wave theory.
Thomas Young proposed that if light is a wave, then it would be possible for light to have diffraction and interference effects, as was known for sound. And he proposed an experimental test: the double-slit experiment, where light would go through two slits and be allowed to combine on the other side, forming alternating light and dark bands. He was supposedly the first person to do that, and success in making that observation discredited the particle theory.
The particle theory was not revived until a century after his work, as a result of the development of quantum mechanics. And according to that theory, not just light, but, everything, behaves like both a particle and like a wave. This wave-particle duality is bizarre and counterintuitive, but abundantly verified at atomic size scales and smaller. And on larger scales, one aspect dominates over another, with macroscopic entities being either particlelike or wavelike.
