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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.

Qmechanic
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TheQuantumMan
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    Would [hsm.se] be a better home for this question? – Qmechanic Jun 06 '15 at 17:21
  • @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. – David Z Jun 06 '15 at 17:22
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    Possible duplicate: http://physics.stackexchange.com/q/18998/2451 – Qmechanic Jun 06 '15 at 17:26
  • No because I am asking about the steps that led to the finding of the equation.I mean the physical steps like it describes a wave so it must look like the general wave equation..I just dont know the other steps.I dont care about timelines or other events or discoveries that lead him there, only the physical or mathematical meaning of each step.Do you want me to clarify this in the question? – TheQuantumMan Jun 06 '15 at 17:27
  • He tried from the klein-gordan equation first-no math here,see-which is harmless enough, then gave up on it, and tried to simplify it, which he did, as far as I know. –  Jun 06 '15 at 17:33
  • As a grammatical aside, there should be one space after punctuation (except the hyphen with no spaces). – Kyle Kanos Jun 06 '15 at 17:33
  • @AcidJazz: Yes, adding spaces improves readability. – Kyle Kanos Jun 06 '15 at 17:45
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    The non-math section of this might be of help, http://en.wikipedia.org/wiki/Schr%C3%B6dinger_equation –  Jun 06 '15 at 17:51
  • @AcidJazz it looks like a really good source.Thank you – TheQuantumMan Jun 06 '15 at 17:58
  • Trying to get both the grammar and the physics right (sorry Kyle:) is difficult. As far as I am aware, it is not too far off the mark to say that the S.E. is the simply the normal F = ma law with what they used to call the quantum prescription applied, that is, make a quantum version of it. –  Jun 06 '15 at 18:06
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    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. – CuriousOne Jun 06 '15 at 20:25

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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.

Victor Buendía
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  • You are correct of course, based on his papers, but wiki does not stress your point about HJ equation, http://en.wikipedia.org/wiki/Klein%E2%80%93Gordon_equation , just wonder why they left it out, it should be included. –  Jun 06 '15 at 18:30