DD pseudo-bosons in quantum models

•We consider some examples of non-self-adjoint Hamiltonians having real eigenvalues.•We show that DD-pseudo-bosons provide an unifying settings for those Hamiltonians.•We conclude that for Hamiltonians with linear real eigenvalues, DD-pseudo-bosons provide the natural description.

We show how some recent models of PT-quantum mechanics perfectly fit into the settings of DD pseudo-bosons, as introduced by one of us. Among the others, we also consider a model of non-commutative quantum mechanics, and we show that this model too can be described in terms of DD pseudo-bosons.