In quantum mechanics, the collapse of the wavefunction occurs when a measurement is made on a quantum system. The collapse of the wavefunction refers to the sudden transition of a superposition of states into a single definite state as a result of the measurement.
The basis to which the wavefunction collapses depends on the specific measurement being performed. Each measurement corresponds to an observable quantity, such as position, momentum, energy, or spin. Each observable has its associated set of eigenstates, which form a basis for the Hilbert space of the system.
When a measurement is made on a quantum system, the wavefunction collapses to one of the eigenstates of the corresponding observable. The probability of the collapse occurring to a particular eigenstate is given by the squared magnitude of the corresponding coefficient in the superposition of states.
For example, if the measurement being performed is the position of a particle, the wavefunction will collapse to one of the position eigenstates. The probability distribution of finding the particle at different positions is given by the squared magnitude of the coefficients associated with each position eigenstate.
It's important to note that the collapse of the wavefunction is a fundamental aspect of quantum mechanics, but the exact interpretation and mechanism behind it are still subject to debate and different interpretations exist, such as the Copenhagen interpretation, the many-worlds interpretation, and the consistent histories interpretation. These interpretations provide different perspectives on how to understand and interpret the wavefunction collapse.