So all of the people who studied QM know the famous Schrödinger equation. I have read that it was not derived, but it is a postulate; something that is just real.
Some people have tried to explain to me that it comes from another more general (I think) equation that has to do with the Hamiltonian, but please do not try to explain it to me that way because then it just becomes maths (if there isn't another explanation then just tell me so).
So physically, intuitively, how did he come up with this? It is a postulate, yes, but nonetheless, Schrodinger did not wake up one day and suddenly knew what the equation was.
Answer
Of course, now we've adopted Schrödinger equation as a postulate: it is true. However, Schrödinger derived the equation from previous knowledge. Schrödinger thought his equation from Hamilton-Jacobi formalism. If you take the classical limit in that equation you'll find the Hamilton-Jacobi equation.
You can also read the original Schrödinger papers in English introducing his wave mechanics formalism. They're the best answer to this question: papers I, II, III and IV.
Note that, however, this is not a demonstration of SE as we understand now. The difference is that Schrödinger derived it from other theories, which relies on assumptioms/conditions. But if you accept the SE as a postulate you combine the equation with some new postulates and old derivations are discarded.
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