On continuous movement of the discrete spectrum of Schr\"odinger operators

Continuous movement of discrete spectrum of the Schr"{o}dinger operator $H(z)=-\frac{d^2}{d{x}^2}+V_0+z{V}_1$, with $\int_0^\infty {x |V_j(x)| dx} < \infty$,onthehalf-lineisstudiedas$z$ 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.