The concept that particles can exhibit wave-like properties is a fundamental aspect of quantum mechanics. It is important to note that when we talk about particles behaving as waves, we are referring to the wave-particle duality at the microscopic scale, where the behavior of matter is governed by quantum mechanics.
The wave-particle duality does not mean that particles exist as both waves and particles simultaneously in the same sense. Instead, it implies that particles can exhibit properties of both particles and waves, depending on how they are observed or measured.
In quantum mechanics, particles are described by wavefunctions, which are mathematical descriptions that contain information about the probability distribution of the particle's properties, such as position, momentum, and energy. The wavefunction describes the wave-like nature of the particle and allows us to calculate the probabilities of finding the particle in different states.
When a measurement is made, the wavefunction collapses to a specific value corresponding to the observed outcome. This collapse results in a particle-like behavior, where the particle is localized at a specific position or has a definite value for a particular property.
The idea that particles cannot occupy the same space at once is a principle known as the Pauli exclusion principle, which applies to fermions (particles with half-integer spin, such as electrons). This principle states that no two identical fermions can occupy the exact same quantum state simultaneously. This principle ensures the stability of matter and plays a crucial role in determining the electronic structure of atoms, among other phenomena.
In summary, particles can exhibit wave-like properties described by wavefunctions, which capture the probabilistic nature of quantum mechanics. The wave-particle duality does not mean that particles exist as both waves and particles simultaneously, but rather that they can exhibit characteristics of both depending on the experimental context. The Pauli exclusion principle prevents identical fermions from occupying the same quantum state, ensuring the stability of matter.