Page "Few-body systems" Paragraph 1

In quantum mechanics, examples of few-body systems include light nuclear systems ( that is, few-nucleon bound and scattering states ), small molecules, light atoms ( such as helium in an external electric field ), atomic collisions, and quantum dots.

A fundamental difficulty in describing few-body systems is that the Schrödinger equation and the classical equations of motion are not analytically solvable for more than two mutually interacting particles even when the underlying forces are precisely known.

This is known as the few-body problem.

For some three-body systems an exact solution can be obtained iteratively through the Faddeev equations.

It can be shown that under certain conditions Faddeev equations should lead to Efimov effect.

Some special cases of three-body systems are amenable to analytical solutions ( or nearly so )-by special treatments-such as the Hydrogen molecular ion whose eigenenergies can be given in terms of a generalized Lambert W function or the Helium atom which has been solved very precisely using basis sets of Hylleraas or Frankowski-Pekeris functions ( see references of the work of G. W. F.

Drake and J. D.

Morgan III in Helium atom section ).