The concept of particles being "wave-packets" arises from quantum mechanics, which is the branch of physics that describes the behavior of particles at the microscopic level. In quantum mechanics, particles are described by wavefunctions, which are mathematical functions that exhibit wave-like properties.
The wave-particle duality is a fundamental principle in quantum mechanics, stating that particles can exhibit both wave-like and particle-like characteristics depending on how they are observed or measured. This means that particles, such as electrons or photons, can display behaviors traditionally associated with waves, such as interference and diffraction.
When we say that particles are "wave-packets," we mean that their wavefunctions are not spread out uniformly but are localized in space. A wave-packet represents a localized disturbance or concentration of a particle's probability amplitude. It combines features of both a wave and a particle, where the wave-packet represents the probability distribution of finding the particle at different positions.
The concept of frequency and wavelength in the context of particles is related to the de Broglie hypothesis, which states that particles, in addition to their particle-like properties, also have a wave nature associated with them. According to this hypothesis, particles have a wavelength associated with their momentum, given by the de Broglie wavelength:
λ = h / p
where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle.
So, while particles in the classical sense may not have traditional wave-like amplitudes, they can exhibit wave-like behavior described by their wavefunctions and associated wavelength and frequency. It is important to note that the wave-particle duality is a complex concept that goes beyond classical intuition and requires the formalism of quantum mechanics to fully understand and describe the behavior of particles at the microscopic level.