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