In quantum mechanics, the wave function describes the state of a quantum system. When an observer measures a particular property of the system, such as position or momentum, the act of measurement causes the wave function to undergo a process called wave function collapse or wave function reduction.
According to the Copenhagen interpretation, which is one of the widely accepted interpretations of quantum mechanics, the act of measurement forces the system to "choose" a specific eigenstate associated with the property being measured. This choice is random and governed by the probabilities described by the wave function. After the measurement, the wave function collapses into the eigenstate corresponding to the observed value.
Mathematically, if the wave function before the measurement is described by a superposition of different eigenstates, the act of measurement causes the system to "select" one of those eigenstates with a probability proportional to the squared magnitude of its coefficient in the superposition. This selection of an eigenstate represents the outcome of the measurement.
It's important to note that the process of wave function collapse is still a topic of philosophical and interpretational debate in quantum mechanics. Other interpretations, such as the many-worlds interpretation, propose different explanations for the measurement process, suggesting that the wave function does not actually collapse but rather branches into different parallel universes representing all possible measurement outcomes.
Nonetheless, the Copenhagen interpretation provides a useful framework for understanding the probabilistic nature of quantum measurements and the collapse of the wave function upon observation.