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On the Qualitative Theory of Non-Gamov Decay States

V. M. Chabanov·B. N. Zakhariev
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Abstract

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.

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V. M. Chabanov, B. N. Zakhariev. 2000-11-30. On the Qualitative Theory of Non-Gamov Decay States. https://arxiv.org/abs/quant-ph/0011119

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