The collapse of the wave function in quantum mechanics refers to a fundamental concept that occurs during the process of measurement. When a quantum system is measured, its wave function, which describes the probabilities of different possible states, appears to "collapse" to a particular state corresponding to the measurement outcome.
The collapse of the wave function is mathematically described by the process of wave function collapse or projection postulate. According to this postulate, when a measurement is made on a quantum system, the system's wave function collapses to one of the eigenstates of the observable being measured. An eigenstate represents a definite value of the observable. For example, if the observable is the position of a particle, the wave function collapses to a specific position eigenstate.
The collapse of the wave function is a non-deterministic process, meaning that the outcome of the measurement is inherently probabilistic. The probability of the collapse yielding a particular eigenstate is given by the square of the amplitude of that eigenstate in the original wave function.
The exact mechanism or physical interpretation of the wave function collapse is still a topic of philosophical and interpretational debates in quantum mechanics. Several interpretations exist, including the Copenhagen interpretation, the many-worlds interpretation, and the consistent histories interpretation, among others. These interpretations offer different perspectives on how to understand the collapse process and its implications.
It's important to note that the collapse of the wave function is a distinct feature of quantum mechanics and differentiates it from classical physics. In classical physics, measurements are expected to yield precise values, whereas in quantum mechanics, the measurement outcomes are inherently probabilistic and involve the collapse of the wave function.