I recall a famous quote of the late physicist Richard Feynman:
Where did we get that from? It's not possible to derive it from anything you know. It came out of the mind of Schrödinger.
This quote was with reference to the derivation of Schrödinger's equation. I often found it strange that, to the best of my knowledge, there was no rigourous method to derive Schrödinger's equation. The closest I've come to finding one was in this paper. Is Feynman's quote still true? Is it not possible to derive Schrödinger's equation from "anything we know." If yes, why is it so widely accepted as the equation that perfectly describes quantum states? Because it coincides with experimental results?