Measurement in quantum mechanics is a fundamental process that allows us to extract information about the state of a quantum system. When a measurement is performed on a quantum system, it causes the system to "collapse" into one of its eigenstates, corresponding to a specific measurement outcome. The collapse is a sudden and irreversible change in the state of the system.
The effect of measurement on the state of a system is described by the collapse postulate, also known as the measurement postulate, in quantum mechanics. According to this postulate, when a measurement is made on a quantum system, the system's state "collapses" into one of the eigenstates of the measured observable, with each eigenstate associated with a particular measurement outcome. The probability of the system collapsing into a specific eigenstate is given by the Born rule, which states that the probability is proportional to the squared magnitude of the projection of the system's initial state onto that eigenstate.
After the measurement, the system is in the eigenstate corresponding to the observed measurement outcome. This means that subsequent measurements of the same observable will always yield the same result as the first measurement. However, if subsequent measurements are made on a different observable, the system will generally not be in an eigenstate of that observable, and the outcome of the measurement will be probabilistic according to the new observable's eigenstates.
It is important to note that measurement disturbs the quantum system and can alter its subsequent evolution. This is known as the measurement problem in quantum mechanics, which is a topic of ongoing debate and interpretation. Various interpretations of quantum mechanics propose different explanations for the measurement process and the apparent collapse of the wavefunction. These interpretations include the Copenhagen interpretation, many-worlds interpretation, and de Broglie-Bohm theory, among others.