Schroedinger operator with weakly accelerating potential

Conceptions of the scattering theory were used for construction of an unitary operator, which realized the equivalence of the operator $-id/d\xi$ on $L_2(\mathbb{R})$ and the Schroedinger operator on simi-axis with the potential $v(x)$, admitting the estimate $-v_-x^{2d}\leq v(x)\leq-v_+x^{2d}$, $v_+>0$, $0<\alpha<1$.