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Electromagnetic radiation, such as light, exhibits both wave-like and particle-like properties. This was demonstrated by various experiments, including Young's double-slit experiment, which showed the interference patterns characteristic of wave behavior, and the photoelectric effect, explained by Einstein, which demonstrated particle-like behavior in the form of photons.

In 1924, Louis de Broglie extended the concept of wave-particle duality to all particles, specifically to tiny particles such as electrons. He hypothesized that all particles of matter, including electrons, have both wave-like and particle-like properties. This is known as the de Broglie hypothesis. According to his hypothesis, the wavelength of a particle is inversely proportional to its momentum, given by the formula: \( \lambda = \frac{h}{p} \) where \( \lambda \) is the wavelength of the particle, h is the Planck's constant, and p is the momentum of the particle.

In 1926, Erwin Schrödinger developed a wave equation, known as the Schrödinger equation, which describes the wave-like behavior of particles in a quantum system. The equation gives the probability distribution of particles in a system, incorporating both their wave-like and particle-like properties. Schrödinger's work built upon de Broglie's hypothesis and provided a mathematical framework for quantum mechanics. In conclusion, the major assumption made by de Broglie and Schrödinger about the motion of tiny particles was that they possess both wave-like and particle-like properties, analogous to the behavior of electromagnetic radiation. This assumption led to the development of the concept of wave-particle duality and the formulation of quantum mechanics.