Wave-particle duality is a fundamental concept in quantum mechanics that describes the dual nature of particles, such as electrons and photons. It suggests that these particles can exhibit both wave-like and particle-like properties, depending on the context of the experiment.

On one hand, particles exhibit characteristics of waves. This is evident in phenomena such as diffraction and interference, where particles can spread out and interfere with each other like waves. For example, in the famous double-slit experiment, electrons or photons are observed to create interference patterns on a screen, indicating their wave-like nature.

On the other hand, particles also exhibit characteristics of localized, discrete entities with definite positions and momenta. This is evident in phenomena such as the photoelectric effect, where photons behave as discrete packets of energy (quanta) when interacting with matter, and in particle detectors that detect individual particles arriving at specific locations.

Wave-particle duality challenges the classical notion of particles as distinct, localized entities and waves as continuous, spread-out phenomena. Instead, it suggests that at the quantum level, particles possess properties of both waves and particles simultaneously. The behavior of particles is described by wavefunctions in quantum mechanics, which encode the probability amplitudes for various states of the particles.

Wave-particle duality is a cornerstone of quantum mechanics and has profound implications for our understanding of the nature of reality at the microscopic scale. It highlights the inherently probabilistic nature of quantum systems and underscores the need for a new conceptual framework to describe the behavior of particles in such systems.