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The wave-particle duality of light is a fundamental concept in physics that was first proposed in the early 20th century. According to quantum mechanics, which is the theory that describes the behavior of particles and waves on a microscopic scale, particles such as photons (which are particles of light) can exhibit both wave-like and particle-like properties.

The understanding of why light behaves as a wave in some experiments and as a particle in others is based on the principles of quantum mechanics. In the early 1900s, experiments such as the double-slit experiment and the photoelectric effect led to the development of the concept of wave-particle duality.

In the double-slit experiment, when light is passed through two narrow slits, an interference pattern is observed on a screen behind the slits, similar to what is observed with water waves passing through two slits. This behavior is characteristic of waves. On the other hand, in the photoelectric effect, light is observed to eject electrons from a material in discrete packets of energy (quanta), which behaves like particles.

The wave-particle duality arises from the mathematical formalism of quantum mechanics, which describes particles and waves using wavefunctions. The behavior of particles such as photons is governed by the Schrödinger equation, which is a fundamental equation in quantum mechanics. The wave-like and particle-like behaviors of light can be understood by considering the wavefunction and its associated probabilities.

In quantum mechanics, the wavefunction describes the probability distribution of finding a particle in a particular state. When measurements are made, the wavefunction "collapses" to a specific value, which corresponds to the observed particle-like behavior. However, when measurements are not made and the system is in a superposition of states, the wave-like behavior dominates.

It is important to note that the wave-particle duality is not limited to light. It applies to all particles in the quantum realm, such as electrons and other subatomic particles. The understanding of this duality has been extensively tested and verified through numerous experiments and is now a well-established aspect of quantum mechanics. However, the underlying philosophical and interpretational aspects of quantum mechanics are still a subject of debate among physicists.

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