According to quantum mechanics, particles can exist in a state called a wavefunction, which describes the probability distribution of finding the particle in different states, such as different positions or energy levels. This wavefunction can be thought of as a "probability wave" that encompasses the various possible states of the particle.
The behavior of particles at the quantum level is often described as wave-particle duality. This means that particles, such as electrons or photons, can exhibit both wave-like and particle-like properties depending on the experimental setup or observation. When a particle is not being observed or its position is not measured, it can be in a superposition of states, meaning it can exist in multiple states simultaneously.
One of the famous examples of this phenomenon is the double-slit experiment. In this experiment, when particles such as electrons or photons are sent through a barrier with two slits, they form an interference pattern on a screen, as if they behaved like waves. However, when the particles are observed or their position is measured, they behave like particles and no longer form an interference pattern.
This experimental result demonstrates that particles can exist as waveforms without being observed or having their position measured. The wave-like behavior is inherent to the quantum nature of particles and is described by the mathematics of quantum mechanics.