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Particles and waves have distinct properties that differentiate them from each other. Here are some key properties associated with particles that are not typically associated with waves:

  1. Discrete Nature: Particles are characterized by their discrete and localized existence. They can be detected and observed at specific positions in space. For example, you can observe the position of a particle by interacting with it, such as through a measurement or a collision.

  2. Mass and Rest Energy: Particles have mass and associated rest energy. Mass is an intrinsic property of particles that determines their inertia and gravitational interaction. Waves, on the other hand, do not possess rest mass.

  3. Particle Interactions: Particles can interact with each other through various fundamental forces, such as electromagnetic, gravitational, weak, and strong forces. These interactions can lead to the exchange of energy, momentum, and other properties between particles.

  4. Particle Statistics: Particles obey different statistical behaviors based on their quantum nature. For example, fermions, which include particles like electrons and protons, follow Fermi-Dirac statistics and exhibit the Pauli exclusion principle, which states that no two fermions can occupy the same quantum state simultaneously. Bosons, such as photons, follow Bose-Einstein statistics and can occupy the same quantum state.

  5. Quantized Properties: Particles exhibit quantized properties, meaning that certain physical quantities, such as energy, angular momentum, and charge, can only take discrete values or multiples of a fundamental unit. This is a characteristic feature of particles described by quantum mechanics.

It's important to note that in the realm of quantum mechanics, particles can also exhibit wave-like properties, known as wave-particle duality. This duality refers to the fact that particles can exhibit both particle-like and wave-like behaviors depending on the experimental context. This behavior is captured by the wave function, which describes the probabilistic distribution of the particle's properties.

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