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.

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    $\begingroup$ Would History of Science and Mathematics be a better home for this question? $\endgroup$
    – Qmechanic
    Jun 6, 2015 at 17:21
  • $\begingroup$ @Qmechanic I don't have strong feelings one way or the other, but that seems plausible. It may also be a duplicate of a question already on this site, but I don't see any obvious candidates in the sidebar. $\endgroup$
    – David Z
    Jun 6, 2015 at 17:22
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    $\begingroup$ Possible duplicate: physics.stackexchange.com/q/18998/2451 $\endgroup$
    – Qmechanic
    Jun 6, 2015 at 17:26
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    $\begingroup$ The non-math section of this might be of help, en.wikipedia.org/wiki/Schr%C3%B6dinger_equation $\endgroup$
    – user81619
    Jun 6, 2015 at 17:51
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    $\begingroup$ I think you should try to read Schroedinger's papers ("Quantisierung als Eigenwertproblem"). There are three parts to the paper and I have never been able to make any real sense of two of them, but then there is the actual Schroedinger equation paper and it's beautiful, simple and absolutely to the point. When you read that it really doesn't matter how he got there, you just instantly know that this is the hand of a genius summarizing in one short note what probably took him years to understand. $\endgroup$
    – CuriousOne
    Jun 6, 2015 at 20:25

1 Answer 1


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.

  • $\begingroup$ You are correct of course, based on his papers, but wiki does not stress your point about HJ equation, en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation , just wonder why they left it out, it should be included. $\endgroup$
    – user81619
    Jun 6, 2015 at 18:30

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