I am reading about Hartree-Fock solution for one atom. It had been said in my book that the Shrodinger equation cant be solved precisely for multi-electron system because of computational dificulties and that is why we should used Hatree=Fock approximation. i am woundering is it really so. the hamiltonian for an atom is: HФ = [ Sum ( Ti + 1/2 Sum (e^2/ |ri - rk| ) - Ze^2/ri ) + 1/2Sum f( xi ..... xk) Ф(xi.....xk) = EФ Ti = -h^2 * (Laplace operator) / 2m, Ф(xi.....xk) the wavefunction for the whole atom xi - electron coordinates E - atom's energy the sum is from zero to Ne - the number of the electrons in the atom I think that this multi-dimensional Shrodinger equation can be solved exactly. Why people use Hartree-Fock and other approximations?
If you think it can, go ahead and solve it! This, much like the classical multi-body gravtation problem, is a non-linear equation and non-linear differential equations are, generally, impossible to solve exactly.
