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Schrodinger Equation!

  1. Nov 13, 2009 #1
    Hey guys,

    I am trying to understand where did this equation exactly come from. I know it is very complex, but anyone can explain it to me in the best way possible?
  2. jcsd
  3. Nov 13, 2009 #2


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    Staff: Mentor

  4. Nov 13, 2009 #3
    Yes please. I think most people who are trying to learn QM want to ask that question. In most Physics textbooks, it's just mentioned that it can't be proved. But are there any plausible explanations as to how the guy came up wit that equation?
  5. Nov 13, 2009 #4


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    Well, of course it can't be proven - this is physics, not pure math.

    But IIRC, Schrödinger made some assumptions but basically 'guessed it'. It was first later that it was derived more rigorously from more basic postulates. This is covered in some more advanced QM textbooks (e.g. first chapter of Landau-Lifschitz)

    I'm embarrassed I can't remember it all, but you assume a system is described by a wave function, which is continuous, square-integrable and normalized. That the observable properties of the system correspond to eigenvalues of Hermitian operators on that wave function, etc.
    (What've I forgotten?)
  6. Nov 13, 2009 #5
    Gaelilean symmetries: spatial and temporal translational invariance, stuff like that. See e.g. the book by Ballentine.
  7. Nov 13, 2009 #6
    The whole process, including the historical context, is described in Valentini and Bacciagaluppi's recent book, available online here:


    or on Amazon if you want to buy it.

    See section 2.3 p.57 onwards. The relevant bit starts "On 3rd November 1925, Schroedinger wrote to Einstein: 'A few days ago I read with the greatest interest the ingenious thesis of Louis de Broglie...'"
    Last edited by a moderator: Apr 24, 2017
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