$\mathcal{D}$ pseudo-bosons in quantum models

We show how some recent models of PT-quantum mechanics perfectly fit into the settings of $\mathcal{D}$ 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 $\mathcal{D}$ pseudo-bosons.