Variation problem in Schrödinger's first paper

1. Oct 6, 2011

inlidos

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:

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[$\nabla$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