Approximation Methods

Compared to the simplified one-dimensional systems or even to the one electron atom, multi-electron atoms are quite complicated. It is possible to treat them in a reasonable way using a succession of approximations. Only the most important interactions experienced by the atomic electrons are treated in the first approximation, and then the treatment is made more exact in succeeding approximations that take into account the less important interactions. Even in the first approximation we must also consider the coulomb interactions between each electron and all the other electrons in the atom. The time independent Schrodinger equation for the system can be separated into a set of equations, one for each electron, which can be solved without too much difficulty, since each involves the coordinates of a single electron only.