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Variation problem in Schrödinger's first paper

  1. Oct 6, 2011 #1
    1. The problem statement, all variables and given/known data
    I am reading Shrödinger's first paper and have some problems understanding it. This is the first step I don't follow. The below is for Keplerian motion and comes from the Hamilton-Jacobi equation. This is what is said:

    Our variation problem then reads

    δJ=δ∫∫∫dxdydz[(∂ψ/∂x)2+(∂ψ/∂y)2+(∂ψ/∂z)2-(2m/K2)(E+e2/r)ψ2]=0,

    the integral being taken over all space. From this we find in the usual way

    (1/2)δJ=∫dfδψ(∂ψ/∂n)-∫∫∫dxdydzδψ[[itex]\nabla[/itex]2ψ+(2m/K2)(E+e2/2)ψ]=0.

    df is an element of the infinite closed surface over which the integral is taken.


    2. Relevant equations
    See above.


    3. The attempt at a solution

    Through partial integration of the squared derivatives I get the term with the tripple integral to fit. What I get apart from this term is

    δ∫∫[(∂ψ/∂x)ψ]dydz+δ∫∫[(∂ψ/∂y)ψ]dxdz+δ∫∫[(∂ψ/∂z)ψ]dxdy.

    Is this somehow the same as ∫dfδψ(∂ψ/∂n)? What is in fact n here? And where does the half in front of δJ come from?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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