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

In classical physics, particles were traditionally considered to have purely particle-like behavior, while waves, such as light or sound waves, were described as having purely wave-like behavior. However, quantum mechanics revolutionized this understanding by showing that particles and waves are not fundamentally distinct entities, but rather different aspects or manifestations of the same underlying physical phenomena.

The wave-particle duality is mathematically described by the wave function in quantum mechanics. The wave function is a mathematical function that characterizes the quantum state of a particle. It can exhibit wave-like properties, such as interference and diffraction, which are typically associated with waves. At the same time, when a measurement is made, the wave function collapses, and the particle is observed at a specific location, exhibiting particle-like behavior.

The wave-particle duality is closely related to the concept of superposition, which is another key aspect of quantum mechanics. Superposition states that a particle can exist in multiple states or positions simultaneously until it is measured or observed, at which point it "chooses" a particular state or position.

The famous double-slit experiment illustrates the wave-particle duality. In this experiment, when a beam of particles, such as electrons or photons, is passed through two slits, an interference pattern is observed on the screen behind the slits, similar to what would be expected for a wave. However, when individual particles are detected, they appear as localized particles, as if they traveled through one of the slits.

Overall, wave-particle duality is a central concept in quantum mechanics that recognizes the inherent dual nature of particles, incorporating both wave-like and particle-like behaviors, and it forms the basis for understanding and interpreting various quantum phenomena.

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