Measurement plays a fundamental role in quantum mechanics. In quantum theory, the act of measurement causes a quantum system to "collapse" from a superposition of multiple possible states into a single definite state. This collapse is known as the "measurement postulate" or the "projection postulate" in quantum mechanics.
Quantum mechanics describes physical systems in terms of wavefunctions, which are mathematical functions that represent the probabilities of different outcomes of a measurement. The square of the wavefunction, called the probability density, gives the probability of finding the system in a particular state upon measurement.
When a measurement is made on a quantum system, the system interacts with the measuring device, and the wavefunction of the system collapses to one of the possible eigenstates of the measured observable. The measurement outcome is one of the eigenvalues associated with the corresponding eigenstate.
The process of measurement in quantum mechanics is inherently probabilistic. Before a measurement is made, a quantum system can exist in a superposition of multiple states, meaning it can be in a combination of different possibilities. However, upon measurement, the system "chooses" one of those possibilities at random according to the probabilities determined by the wavefunction.
Measurement in quantum mechanics is a subject of ongoing research and philosophical debate. The nature of the measurement process and the interpretation of quantum mechanics have been studied by various interpretations such as the Copenhagen interpretation, the many-worlds interpretation, and the consistent histories interpretation, among others.