Solvable quantum lattices with nonlocal non-Hermitian endpoint interactions
arXiv:1506.00216 · doi:10.1016/j.aop.2015.06.019
Abstract
Discrete multiparametric 1D quantum well with PT-symmetric long-range boundary conditions is proposed and studied. As a nonlocal descendant of the square well families endowed with Dirac (i.e., Hermitian) and with complex Robin (i.e., non-Hermitian but still local) boundary conditions, the model is shown characterized by the survival of solvability in combination with an enhanced spectral-design flexibility. The solvability incorporates also the feasibility of closed-form constructions of the physical Hilbert-space inner products rendering the time-evolution unitary.
32 pages, 9 figures
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