If we measure a Quantum state with result , Then immediately after the Measurement, the system will be in a state satisfying Where is the Self-Adjoint Operator associated with .


If a quantum system is described by a Quantum state , the probability distribution of the Classical observable is given by


Although we are in a Quantum Hilbert Space, we still care about measuring Classical observables. Rather than having a deterministic Classical observable value, a quantum system state gives us a probability distribution for the classical counterpart.