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Quantum mechanics is a branch of physics that provides a mathematical framework to describe the behavior of particles at the subatomic level, such as electrons, protons, and photons. It is a fundamental theory that incorporates the principles of wave-particle duality, superposition, and uncertainty.

At the heart of quantum mechanics is the concept of wave-particle duality, which suggests that particles can exhibit both wave-like and particle-like properties depending on how they are observed. This means that subatomic particles, such as electrons, can exhibit characteristics of both particles and waves simultaneously.

Quantum mechanics uses mathematical objects called wavefunctions to describe the state of a particle. The wavefunction represents the probability amplitude of finding a particle in a particular state. It contains information about the particle's position, momentum, energy, and other observable properties.

One of the key features of quantum mechanics is superposition. Superposition states that particles can exist in multiple states simultaneously. For example, an electron can be in a superposition of being in two different positions or having two different spin orientations at the same time. However, when a measurement is made, the superposition "collapses" into a single state with a definite value.

Another crucial concept in quantum mechanics is uncertainty, as described by Heisenberg's uncertainty principle. The uncertainty principle states that there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be known simultaneously. This means that the more accurately we try to measure one property, the less precisely we can know the other property.

Quantum mechanics also involves the idea of quantum entanglement, where two or more particles become correlated in such a way that the state of one particle cannot be described independently of the state of the other, regardless of the distance between them. This phenomenon has been experimentally verified and is the basis for various applications in quantum information and quantum communication.

Overall, quantum mechanics provides a probabilistic framework that describes the behavior of subatomic particles and their interactions. It has been incredibly successful in explaining a wide range of phenomena observed in experiments, although it is often considered to have counterintuitive aspects due to its departure from classical physics.

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