The method of effective field theories (EFTs) is developed for the scattering
of two particles at wavelengths which are large compared to the range of their
interaction. It is shown that the renormalized EFT is equivalent to the
effective range expansion, to a Schroedinger equation with a pseudo-potential,
and to an energy expansion of a generic boundary condition at the origin. The
roles of regulators and potentials are also discussed. These ideas are
exemplified in a toy model.Comment: 38 pages, 6 figure