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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?

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This may be better suited for the Physics Stack Exchange site, since one can only 'derive' Schrodinger's equation based on physical principles. (One can study it mathematically, but the mathematical interest need not be reliant on it being a description of an actual physical phenomenon.) –  Semiclassical Aug 2 at 0:30
    
@Semiclassical I posted it on this site because I was interested in knowing whether there was a actual rigourous derivation for it. –  Millardo Peacecraft Aug 2 at 0:32
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To which I have to respond, a rigorous derivation from what? You can certainly find Schrodinger's equation in mathematical contexts, but its meaning as a description of (non-relativistic) quantum mechanics is not something one derives: it is something one theorizes and applies. (One can ask about how it arises as an approximation of quantum field theory, for example, but such will remain a physical argument and not an essentially mathematical one.) –  Semiclassical Aug 2 at 0:36
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Perhaps a derivation is the wrong word. Maybe you want an interpretation. I think you can interpret the equation as conservation of energy written as an operator equation. –  James S. Cook Aug 2 at 0:50
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It is possible, but it requires you to make other assumptions about the behaviour of quantum systems. Why do you find this surprising though? There are many physics equations that cannot be derived, these are known as postulates. You choose postulates because they seem to capture how nature works. Maxwell's equations can't be derived from the perspective of classical electrodynamics (they can be derived from quantum electrodynamics, but then you're just choosing other postulates to begin with). At some point though, you have to choose an equation(s), simply because it seems to work. –  user46080 Aug 2 at 2:26

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I think there is a post almost identical with yours at here:

http://physics.stackexchange.com/questions/30537/is-the-schr%C3%B6dinger-equation-derived-or-postulated

but there is a much better answer at here:

http://physics.stackexchange.com/questions/83450/is-it-possible-to-derive-schrodinger-equation-in-this-way/83458#83458

I had the same question myself when I reading Feynman a few months ago.

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