The core of understanding the wave-particle duality in quantum mechanics lies in recognizing that particles, such as electrons or photons, exhibit behaviors that can be described by both wave-like and particle-like characteristics. This duality challenges our classical intuition, where objects are usually thought of as either particles or waves.
At the heart of quantum mechanics is the concept of a wave function, denoted by the Greek letter Ψ (psi). The wave function describes the state of a quantum system and contains information about the probabilities of different outcomes when properties of the system are measured. It is a mathematical function that evolves over time according to specific equations, such as the Schrödinger equation.
When we consider particles like electrons or photons, their wave-like behavior is described by the wave function. This wave function represents the probability amplitude associated with finding the particle in different states or positions. It exhibits characteristics such as interference, diffraction, and superposition. These phenomena are typically associated with waves, where multiple waves can combine or cancel each other out.
However, when a measurement is made or an interaction occurs, the wave function collapses into a definite state, and the particle-like behavior becomes apparent. The outcome of the measurement corresponds to a specific eigenstate of the system. The collapse of the wave function is instantaneous and random, and it is described by the Born rule, which provides the probabilities for different measurement outcomes.
In summary, the core understanding of the wave-particle duality in quantum mechanics involves recognizing that particles can exhibit wave-like behavior described by a wave function, which encompasses probabilities and interference effects. However, when a measurement is made, the wave function collapses, and the particle manifests as a localized entity with definite properties. The dual nature of particles is a fundamental aspect of quantum mechanics and is supported by extensive experimental evidence.