Postulate 3

Any measurement of an observable \(\hat{Q}\) must yield an eigenvalue \(\lambda \) of \(\hat{Q}\) (solution to the eigenvalue equation \(\hat{Q} |\varPsi _{\lambda }\rangle =\lambda |\varPsi _{\lambda }\rangle \) ). The measurement prepares the system in a state in which \(\hat{Q}=\lambda .\) If the system is in a state \(|\varPhi \rangle ,\) the probability of a particular \(\lambda \)  is \(P(\lambda )=\langle \varPhi | \varPsi _{\lambda }\rangle |^{2}\) . This is known as the Born Rule.