Schrödinger operators with non-symmetric zero-range potentials (Q2877333)

The authors study nonselfadjoint Schrödinger operators corresponding to non-symmetric zero-range potentials. The specific problems they solve include the description of nonreal eigenvalues and spectral singularities, the possibility of interpretations of the above operators as selfadjoint operators on a Krein space, similarity to selfadjoint operators on Hilbert spaces. These problems are motivated by \(\mathcal P\mathcal T\)-symmetric quantum mechanics; see also \textit{S. Albeverio} and \textit{S. Kuzhel} [J. Phys. A, Math. Gen. 38, No. 22, 4975--4988 (2005; Zbl 1070.81048)].