**Analysis of Point Spectrum and the
Inverse Scattering Problem for the Sturm - Liouville Operator with Certain
Behavior of Potential at Infinity**

In the space L^{2}(R) the Sturm -
Liouville operator with certain behavior of potential at infinity is considered.
Its point spectrum was studial and the scattering data were introduced. It is
proved that the potential is uniquely determined by the scattering data and the
question of its recovery is reduced to the linear integral equation.