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Wave-particle duality is a fundamental concept in quantum mechanics and has been experimentally verified through numerous experiments. It refers to the observation that particles, such as electrons or photons, can exhibit both wave-like and particle-like behavior under certain experimental conditions.

The wave-like behavior of particles is not in the sense of physical waves like ocean waves or sound waves but rather in terms of mathematical wave functions. In quantum mechanics, particles are described by wave functions that determine the probability distribution of their properties, such as position, momentum, and energy.

When a particle's wave function is not constrained or observed, it can spread out and exhibit characteristics similar to waves. This is seen in phenomena such as interference and diffraction patterns. For example, in the famous double-slit experiment, when a beam of particles (e.g., electrons or photons) is directed at two slits, an interference pattern is observed on a screen behind the slits. This pattern can only be explained if we consider the particles as having wave-like properties.

However, when a measurement is made to determine the particle's position or other properties, the wave function collapses, and the particle behaves more like a localized particle with specific properties. This is often referred to as the wave function collapsing to a single value.

The exact mechanism behind wave-particle duality is still a subject of ongoing debate and interpretation in quantum mechanics. Various interpretations, such as the Copenhagen interpretation or the many-worlds interpretation, offer different perspectives on how to understand and interpret this duality.

In summary, wave-particle duality is a fundamental aspect of quantum mechanics, where particles can exhibit both wave-like and particle-like behavior depending on the experimental setup and measurement context. The wave behavior is described by mathematical wave functions that determine the probability distribution of the particle's properties.

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