# Where does the postulate of quantum mechanic that possible results are eigenvalues come from? [duplicate]

Where does the idea come from, that possible results of quantum measurement are eigenvalues of the operator corresponding to the observable?

• For those who state that the question is duplicate : it is not the case. The other questions so-called 'duplicate' are discussing about the reason that probability is the square of the eigenvectors. I deal here mostly with reason for choosing eigenvalues as solutions : I don't discuss on the associated probability. Sep 4 '19 at 12:24

Postulates come in a sense from nowhere, but I will make a case. De Broglie proposed that since light can behave as consisting of particles in the photoelectric effect, it would make sense that all particles could behave like waves. This inspired Schrödinger to replace energy and momentum by the well known operators in the classical energy expression $$E=p^2 /2m +V$$. It turned out right. The resulting Schrödinger equation has quantized solutions, so called eigenfunctions, and describes (nonrelativistic) physics correctly. And there you are: nature is quantized.