When two particles interact, the behavior of their wave functions is described by the principles of quantum mechanics. The wave function of a system of particles, such as two interacting particles, represents the probabilistic description of their possible states.
In quantum mechanics, the wave function of a single particle provides information about the probability distribution of finding the particle in different states, such as its position or momentum. When two particles interact, their wave functions become entangled, meaning the description of one particle becomes dependent on the state of the other.
The combined wave function of the two particles is determined by their individual wave functions and the nature of their interaction. The wave function accounts for all possible states of the system, including the entangled states resulting from the interaction.
The evolution of the wave function is governed by the Schrödinger equation or other appropriate equations, depending on the specific system and interaction involved. As the particles interact, their wave functions can become more correlated, leading to entangled states where the behavior of one particle is intimately connected to the behavior of the other.
The entanglement of the wave functions introduces correlations between various observable properties of the particles. For example, the measurement of a property (such as position, spin, or momentum) of one particle can instantaneously affect the corresponding property of the other particle, even if they are physically separated.
It's important to note that the exact details of the interaction and resulting entanglement can vary widely depending on the specific system and forces involved. The behavior of interacting wave functions is a complex and mathematically rigorous topic in quantum mechanics, and it often requires advanced techniques and approximations to study and understand specific cases.
In summary, when two particles interact, their wave functions become entangled, and the combined wave function describes the probabilistic behavior of the system. The interaction leads to correlations between the particles, where the measurement of one particle's properties can influence the properties of the other, even at a distance.