Fate of the Unbound States in Near-infinitely Deep Potential Models

Based on the one-dimensional model with quasi-periodicity and nearly infinite depth potential well, this paper studies how the depth of the potential well and non-Hermiticity affects the unbound states. By extending the Liu-Xia model to a deeper structure, we confirm through calculating IPR and based on Avila's global theory, that although the potential well is deeper, there are still unbound states within specific energy intervals. Extending the research to non-Hermitian systems with gain-loss