Particle and photon waves exhibit oscillatory behavior due to their wave-particle duality, as described by quantum mechanics. The wave-like nature of particles and photons is characterized by a property called the wavefunction, which represents the probability amplitude of finding a particle at a particular location or the state of a photon.
The oscillations arise from the interference of these wavefunctions. When particles or photons are in superposition, meaning they can exist in multiple states simultaneously, their wavefunctions combine and interfere with each other. Interference occurs when waves overlap, leading to constructive or destructive interference depending on the phase relationship between the waves.
In the case of particles, such as electrons or atoms, their wavefunctions can be described by solutions to the Schrödinger equation. These solutions are usually in the form of standing waves, which have nodes and antinodes. The nodes represent points of zero probability density, while the antinodes correspond to regions of higher probability density. The oscillatory behavior arises from the alternation between nodes and antinodes.
For photons, which are quanta of electromagnetic waves, their oscillatory behavior is inherent in the nature of electromagnetic radiation. Photons have a characteristic frequency and wavelength associated with their energy. The oscillations of the electromagnetic field occur as the photon propagates through space, and these oscillations are manifested as waves.
In summary, the oscillatory behavior of particle and photon waves arises from the wave-particle duality in quantum mechanics. It is a result of the interference of wavefunctions and the inherent nature of electromagnetic radiation.