My physics teachers told me that there is no derivation of the Schrödinger Wave Equation and that Schrödinger actually wrote this equation from nothing. He wrote it from his mind. Even in my book there is no rigorous derivation of the Schrödinger Wave Equation. But how is this possible? How did Schrödinger make such a wild guess to such a equation that turns out to be the '$F=ma$' for quantum mechanics? I am pretty sure he hadn't just guessed the equation, right? I mean what are the odds of such a guessed equation to be so fundamentally correct? Why does everyone say that Schrödinger wrote his Schrödinger Wave Equation from his mind? Why?
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Does this answer your question? How can one derive Schrödinger equation? – John Rennie May 25 '21 at 04:37
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2Why does everyone say that Schrödinger wrote his Schrödinger Wave Equation from his mind? They don’t. None of my physics teachers said that. It can’t be derived but it can be motivated. – G. Smith May 25 '21 at 05:02
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It is useful to read Schroedinger's original papers (in German or translated into English) to get an idea of how he ended up with this equation(s). – DanielC May 25 '21 at 07:24
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@DanielC not necessarily translated: Schrödinger appears to have published in PhysRev vol. 28 №6: "An Undulatory Theory of the Mechanics of Atoms and Molecules" (you can easily find PDF versions online). – Ruslan May 25 '21 at 08:33