One-dimensional Schrodinger operators with rho-symmetric zero-range potentials

摘要

Non-Hermitian Hamiltonians appearing as operator realizations of P-symmetric (PT-symmetric in physical literature) zero-range singular perturbations of one-dimensional Schrodinger operators are studied. In particular, Hamiltonians with a real spectrum are described in terms of parameters of singular perturbations and, moreover, it is shown that only part of them are similar to Hermitian ones. In this case, they can be used as exactly solvable models of PT-symmetric quantum mechanics.