On continuous movement of the discrete spectrum of Schrödinger operators

Abstract

Continuous movement of discrete spectrum of the Schrödinger operator $H(z)=-\frac{d^2}{d{x}^2}+V_0+z{V}_1$, 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.

22 pages