Examples of pseudo-bosons in quantum mechanics

Fabio Bagarello, Margherita Lattuca

Fabio Bagarello

Fabio Bagarello, Miloslav Znojil

The increasingly popular concept of a ‘hidden’ Hermiticity of operators is compared with the recently introduced notion of nonlinear pseudo-bosons . The formal equivalence between these two notions is deduced under very general assumptions. Examples of their applicability in quantum mechanics are discussed.

Fabio Bagarello

Fabio Bagarello

We discuss how a q-mutation relation can be deformed replacing a pair of conjugate operators with two other and unrelated operators, as it is done in the construction of pseudo-fermions, pseudo-bosons and truncated pseudo-bosons. This deformation involves interesting mathematical problems and suggests possible applications to pseudo-hermitian quantum mechanics. We construct bi-coherent states associated to D -pseudo-quons, and we show that they share many of their properties with ordinary coherent states. In particular, we find conditions for these states to exist, to be eigenstates of suitable annihilation operators and to give rise to a resolution of the identity. Two examples are discussed in details, one connected to an unbounded similarity map, and the other to a bounded map.

Partha Ghose, Dipankar Home, M.N. Sinha Roy