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I was just wondering this lately: where does the Shrodinger Equation come from? How was it 'invented'?

Our teacher told us that it cannot be derived from any classical mechanics (quite obviously) so how did Shrodinger come up with it?

I can hardly believe he just postulated that a wavefunction would obbey that equation, and it "happened" to obbey measurements..?

I can't find this anywhere, not even in my QM textbook (by Griffiths). Actually the first chapter begins by stating the SE... No explanation whatsoever!

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# Shrodinger Equation, where did it come from?

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