The wave-particle duality is a fundamental concept in quantum mechanics that describes the dual nature of particles. It suggests that particles, such as electrons and photons, can exhibit both wave-like and particle-like behavior depending on how they are observed or measured.
When we say that a particle can exhibit wave-like behavior, it means that its properties can be described by a wave function, which represents the probability distribution of finding the particle in different states or locations. This wave function can have spatial extent, meaning it can spread out over a region of space.
In contrast, when we say that a particle exhibits particle-like behavior, it means that it behaves as a localized entity with well-defined position and momentum. This is typically what we observe in macroscopic objects in everyday life.
Now, in the context of the wave-particle duality, it's important to understand that the wave and the particle are not the same thing but rather different aspects or descriptions of the same underlying quantum entity. The particle-like behavior emerges when we make a measurement or interact with the system in a way that collapses the wave function, forcing the particle to be localized at a particular position.
So, the wave associated with a particle can have a spatial extent because it represents the probability distribution of finding the particle in different regions of space. However, when a measurement is made, the particle manifests as a localized entity at a specific position. The wave-particle duality is a manifestation of the intrinsic probabilistic nature of quantum mechanics, where the behavior of particles is described by waves of probability rather than deterministic trajectories.