According to quantum mechanics, particles can exhibit wave-particle duality, which means they can exhibit characteristics of both particles and waves. This duality is described by wave functions, which are mathematical functions that represent the probability distribution of a particle's properties, such as position or momentum.
Particles can be described as localized entities with definite positions and momenta, which is more in line with their particle nature. However, when particles are not being observed or measured, their behavior is often described by wave-like phenomena. This wave-like behavior is manifested through phenomena such as interference and diffraction.
Furthermore, particles are associated with corresponding quantum fields. According to quantum field theory, each particle is considered an excitation or a quantized disturbance in its corresponding field. For example, the electron is associated with the electron field, and the photon is associated with the electromagnetic field.
In this view, particles can be thought of as localized excitations or "packets" of energy in their respective fields. These fields permeate all of spacetime, and particles can interact with these fields to create observable effects.
So, while particles can exhibit both wave-like and particle-like behavior, it is important to note that they are not literally waves in the sense of classical waves like water waves or sound waves. Instead, the wave-particle duality is a fundamental aspect of quantum mechanics that describes the behavior of particles at the microscopic level.