The continuous spectrum of bound states in expulsive potentials: self-trapping in the linear system
Hidetsugu Sakaguchi [1], Boris A. Malomed* [2]ORCID iD, Andreas C. Aristotelous [3], Efstathios G. Charalampidis [4]
https://www.academia.edu/3064-979X/3/2/10.20935/AcadQuant8294
Introduction: Contrary to common intuition, which suggests that a steep expulsive potential makes quantum states widely delocalized, we demonstrate that one- and two-dimensional (1D and 2D) Schrödinger equations, which include expulsive potentials that are steeper than the quadratic ones, give rise to normalizable eigenstates, which may be considered as a manifestation of effective self-trapping in the linear system.
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