In the context of quantum mechanics, a wave is a mathematical description that represents the probability distribution of finding a particle in different states. It describes the behavior and properties of the particle in a wave-like manner. The wave nature of particles is often referred to as wave-particle duality.
The wave-particle duality suggests that particles, such as bosons, can exhibit both particle-like and wave-like properties depending on the experimental setup and conditions. At cold temperatures, when particles are in a highly ordered state, they can collectively behave as waves. This phenomenon is known as Bose-Einstein condensation.
Bose-Einstein condensation occurs for particles called bosons, which have integer spin (0, 1, 2, etc.). When a gas of bosons is cooled to extremely low temperatures, their individual wavefunctions start to overlap and become coherent. This coherence leads to a macroscopic occupation of the lowest energy state, forming a single collective wavefunction that describes the entire system. In other words, all the particles "condense" into the same quantum state.
At this low temperature regime, the individual bosons lose their distinct identities and behave collectively as waves. The collective wavefunction can exhibit interference phenomena, similar to the interference of waves in classical physics. This behavior is a consequence of quantum statistics and arises from the indistinguishability of identical particles.
Bose-Einstein condensation was first predicted by Satyendra Nath Bose and Albert Einstein in the 1920s, and it has been experimentally observed in certain systems such as ultracold atomic gases. It provides a fascinating example of how particles, at sufficiently low temperatures, can exhibit wave-like properties on a macroscopic scale.