On continuous movement of the discrete spectrum of Schrodinger operators

Continuous movement of discrete spectrum of the Schr{o}dinger operator $H(z)=-frac{d^2} {dx^2}+V_0+z V_1$, with $int_0^infty {x |V_j(x)| dx} < infty$, on the half-line is studied as $z$ moves along a continuous path in the complex plane. The analysis provides information regarding the members of the discrete spectrum of the non-selfadjoint operator that are evolved from the discrete spectrum of the corresponding selfadjoint operator.