$\mathcal D$ -Deformed Harmonic Oscillators

Abstract

We analyze systematically several deformations arising from two-dimensional harmonic oscillators which can be described in terms ofD-pseudo bosons. They all give rise to exactly solvable models, described by non self-adjoint hamiltonians whose eigenvalues and eigenvectors can be found adopting the quite general framework of the so-called D-pseudo bosons. In particular, we show that several models previously introduced in the literature perfectly fit into this scheme.