In a double-slit experiment, which is a classic example of wave-particle duality, a single particle, such as an electron or a photon, is sent through a barrier with two narrow slits and then detected on a screen behind the barrier. Surprisingly, even when particles are sent through one at a time, an interference pattern emerges on the screen, indicating that they exhibit wave-like behavior.
This phenomenon is described mathematically using the wave function, which is a mathematical expression that represents the probability distribution of a particle's properties, such as its position or momentum. Initially, before the particle passes through the slits, its wave function is a superposition of the two possible paths it can take.
However, when a measurement is made to determine the particle's position, such as by placing a detector at the slits or on the screen, the wave function collapses, and the particle is observed at a specific location. This collapse means that the particle's position becomes well-defined at the detection point.
On the other hand, if the measurement is made to determine the particle's momentum, the wave function collapses into a different state where the momentum is well-defined. This would not provide information about the particle's position.
Therefore, after passing through the double-slit experiment and undergoing a measurement to determine either the position or the momentum, the particle's wave function collapses into a state where the measured property (either position or momentum) becomes definite. However, the other property becomes uncertain due to the Heisenberg uncertainty principle, meaning that the particle cannot simultaneously possess both a definite position and a definite momentum.
In summary, the double-slit experiment demonstrates the wave-particle duality of quantum systems, where a particle's behavior can exhibit both wave-like and particle-like characteristics. The particle's properties become definite only when a measurement is made, and the wave function collapses into a corresponding state.