Long-range potential scattering: Converting long-range potential to short-range potential by tortoise coordinate

Inspired by general relativity, we suggest an approach for long-range potential scattering. In scattering theory, there is a theory short-range scattering, but no This because the boundary conditions all potentials are same, different different. this paper, introducing tortoise coordinates, convert to allows us deal with as An explicit expression of wave function presented, in which represented coordinate and phase shift. We show that just replacement common coordinate. The applies not only also bound states. Furthermore, terms classification scheme potentials. discuss duality between coordinates.