The behavior of particles and waves in the realm of quantum mechanics is described by a concept known as wave-particle duality. According to this principle, elementary particles, such as electrons and photons (particles of light), can exhibit both particle-like and wave-like characteristics under different circumstances.
The behavior of a particle or system is governed by its wave function, which is a mathematical representation that describes its quantum state. The wave function can exhibit wave-like properties, such as interference and diffraction, which are typically associated with waves. This is particularly evident in experiments like the double-slit experiment, where particles display interference patterns similar to those observed for waves.
On the other hand, particles also exhibit particle-like behavior when interacting with detectors or when their properties, such as position or momentum, are measured. When particles are detected, they manifest as localized entities with well-defined positions, resembling classical particles.
The nature of the observation or measurement affects the manifestation of either particle-like or wave-like behavior. This phenomenon is encapsulated in the principle of wave-particle duality. The behavior of a particle can be described by its wave function, which evolves according to Schrödinger's equation, and the measurement or observation collapses the wave function to a specific state corresponding to a particle with definite properties.
It's important to note that the wave-particle duality is not limited to subatomic particles. It also applies to larger objects, such as atoms and molecules, although the wave-like behavior becomes less noticeable at larger scales due to the phenomenon of decoherence.
In summary, the behavior of particles and waves is intrinsically interconnected and depends on the experimental setup and observation. Under different circumstances, particles can exhibit wave-like properties, such as interference and diffraction, or particle-like properties, such as localized positions, reflecting the wave-particle duality of quantum mechanics.