Position space Hartree-Fock Equations[1]

The solution of a normal Schroedinger equation in frequency space is considered in SEQNFD.htm .doc. The derivation of and meaning of position space Hartree-Fock equations is considered in HARTREE.htm .doc and HF.htm .doc.

Separating out the terms in r space

Define

Finally equation 11 of the paper written out in detail

Note that this is an algebraic, not a differential equation

Defining

Thus the final equation is

Which is formally the same as equation 12 in ..\wsteve\SEQNFD.htm

Del squared

Hydrogen-like function of r

Assume

So that

So thatand

Relevant integrals Dwit859.htm intis.htm

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[1] S.A. Alexander, R.L. Coldwell, and H.J. Monkhorst, “Polyatomic SCF Calculations with Numerical Orbitals II”,Journal of Computational Physics, 76, pp263-280

(1988).