I'm an undergraduate mathematics student trying to understand some quantum mechanics, but I'm having a hard time understanding what is the status of the Schrödinger equation.
In some places I've read that it's just a postulate. At least, that's how I interpret e.g. the following quote:
Where did we get that (equation) from? Nowhere. It is not possible to derive it from anything you know. It came out of the mind of Schrödinger. -- Richard Feynman
(from the Wikipedia entry on the Schrödinger equation)
However, some places seem to derive the Schrödinger equation: just search for "derivation of Schrödinger equation" in google.
This motivates the question in the title: Is the Schrödinger equation derived or postulated? If it is derived, then just how is it derived, and from what principles? If it is postulated, then it surely came out of somewhere. Something like "in these special cases it can be derived, and then we postulate it works in general". Or maybe not?
Thanks in advance, and please bear with my physical ignorance.