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We consider a simple modification of the 1D-Laplacian where non-mixedinterface conditions occur at the boundaries of a finite interval. It hasrecently been shown that Schr\"odinger operators having this form allow a newapproach to the transverse quantum transport through resonant heterostructures.In this perspective, it is important to control the deformations effectsintroduced on the spectrum and on the time propagator by this class ofnon-selfadjont perturbations. In order to obtain uniform-in-time estimates ofthe perturbed semigroup, our strategy consists in constructing stationary wavesoperators allowing to intertwine the modified non-selfadjoint Schr\"odingeroperator with a 'physical' Hamiltonian. For small values of a deformationparameter '{\theta}', this yields a dynamical comparison between the two modelsshowing that the distance between the corresponding semigroups is dominated by|{\theta}| uniformly in time in the L^2-operator norm.

Wave operators, similarity and dynamics for a class of Schroedinger operators with generic non-mixed interface conditions in 1D