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I Just to check Schrodinger equation with 2 electrons

  1. Aug 5, 2016 #1
    Hi folks,

    I just want to check I understand correctly the Schrodinger equation for two electrons.

    https://en.wikipedia.org/wiki/Schrödinger_equation#Time-independent_equation

    With control F you can find "two electrons atoms or ions" section.

    Let's assume the wave function = x1 2+ x22 and let's test if it satisfies the differential equation. (Instead of position vector r y use only x in 1D and the Laplacian operator is just a derivative respect x):

    E * (x12 + x22) = -h2 * (2/μ) + e2/4piε0 * (1/x2-x1 - Z ( 1/x1+1/x2)) * (x12 + x22)

    In case this equation were true I would have found a solution, Is this correct?
     
    Last edited: Aug 5, 2016
  2. jcsd
  3. Aug 5, 2016 #2

    ZapperZ

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    This is very odd.

    In 1D, you do not get that type of a central potential. You have to solve this in 3D if you want to keep that potential.

    Zz.
     
  4. Aug 5, 2016 #3
    This demonstrates opening this thread was a good idea.

    Do you know any book or thread were the 2 body problem is approached. Since I read it is not solvable I assume nobody is publishing failed attempts. I suppose mathematicians have tried very hard to solve this equation and maybe they don't know how to do it, but for sure they know a lot of ways not to solve it right?

    Where could I learn about this?
     
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