On the Qualitative Theory of Non-Gamov Decay States

Complex potential transformations which add imaginary parts to chosen energy levels are given and qualitatively explained. Unexpected shape similarity of potential perturbations for real and imaginary E-shifts of bound states are exhibited. The imaginary E-shifts in the continuous spectrum lead to a surprising quasi-periodic field raking up initial propagating waves into localized states. Complex periodic potentials without lacunas (!) are constructed. The fission of quasi-bound states when neighbour complex eigenvalues approach one another is demonstrated. E-shift algorithms represent wide classes of exactly solvable quantum models for non-self-adjoint operators.