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The wave-particle duality of light is a fundamental concept in quantum mechanics. It describes the behavior of light and other particles in terms of both wave-like and particle-like properties.

The wave nature of light is observed in phenomena such as interference and diffraction. When light passes through narrow slits or encounters obstacles, it exhibits interference patterns and spreads out like waves do. These behaviors are characteristic of waves and can be described using wave equations, such as the famous wave equation formulated by James Clerk Maxwell to describe electromagnetic waves.

On the other hand, the particle nature of light is demonstrated through phenomena like the photoelectric effect and the observation of discrete energy levels in atomic spectra. The photoelectric effect occurs when light is incident on a material, causing the ejection of electrons. This effect cannot be explained solely by the wave nature of light but requires the concept of photons—particles of light with discrete energy and momentum. Similarly, the observation of discrete energy levels in atomic spectra indicates that light interacts with matter as discrete particles.

The wave-particle duality arises from the principles of quantum mechanics, which describe the behavior of particles at the microscopic level. According to quantum mechanics, particles, including photons, can exist in superposition states, meaning they can simultaneously exhibit wave-like and particle-like properties. The wave-like behavior of particles is described by a mathematical framework called wave functions or quantum wave equations, which determine the probability distribution of a particle's properties, such as position or momentum.

When a measurement is made on a quantum system, it "collapses" the wave function, and the particle behaves like a localized entity, exhibiting specific properties at that moment. This is often referred to as wave function collapse or the observer effect. The measurement outcome corresponds to the particle-like aspect of the system.

The wave-particle duality is not limited to light but is a fundamental property of all elementary particles in the quantum realm, including electrons and other subatomic particles. The behavior of these particles can exhibit both wave-like and particle-like characteristics depending on the experimental setup and the nature of the observation.

In summary, light exhibits wave-like behavior in some experiments (interference, diffraction) and particle-like behavior in others (photoelectric effect). The wave-particle duality is a fundamental aspect of quantum mechanics, reflecting the complementary and sometimes paradoxical nature of the microscopic world.

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