According to quantum mechanics (QM), particles are described by wave-functions that represent their probability distributions in space. These wave-functions can exhibit properties such as interference and superposition, which are characteristic of waves. However, it is important to note that the interpretation of wave-functions and their connection to physical reality is still a subject of debate and different interpretations exist.
In the standard interpretation of QM, particles are treated as point-like entities with no spatial extent or internal structure. The wave-function describes the probability of finding a particle at different positions in space. This probabilistic nature of particles at the quantum level is a fundamental aspect of QM.
However, it is also worth mentioning that at macroscopic scales, the wave-like properties become negligible, and classical mechanics is an effective description of the physical world. In classical mechanics, particles are treated as having definite positions and physical dimensions.
It's important to keep in mind that the concept of "particle" in QM is distinct from the everyday notion of a classical particle. The behavior of particles at the quantum level is better understood by considering them as wave-particle duality, where they can exhibit both wave-like and particle-like characteristics depending on the experimental setup and measurement.
In summary, according to the standard interpretation of QM, particles are described by wave-functions and do not possess definite positions or physical dimensions in the same way classical particles do. They exhibit wave-like behavior and their properties are probabilistic in nature.