In physics at university, I was told that quantum mechanics was based on a number of postulates, two of which were: 1. For every particle moving in a conservative field of force there exists an associated wave function, psi, which determines every property which can be physically measured. In general this is a complex number and represents the state of the system. 2. To every physical observable O, there exists an associated operator O such that Opsi = o*psi, and this equation is solvable for o and a corresponding value of psi. Can anyone please tell me how the second postulate was "thunk up" as it appears to be completely random. I understand that the postulates are justified as they explain physical observations, but how would one even come to develop such a bizaar postulate as postulate 2.