Extended coupled SUSY, pseudo-bosons and weak squeezed states

Abstract

In this paper we consider squares of pseudo-bosonic ladder operators and we use them to produce explicit examples of eigenstates of certain operators satisfying a deformed $\mathfrak{su}(1,1)$ Lie algebra. We show how these eigenstates may, or may not, be square-integrable. In both cases, a notion of biorthonormality can be introduced and analyzed. Some examples are discussed in details. We also propose some preliminary results on bi-squeezed states arising from our operators.

arXiv admin note: text overlap with arXiv:2102.11738

References in corpus (2)

• Ladder operators for Klein-Gordon equation with scalar curvature term
• Bi-coherent states as generalized eigenstates of the position and the momentum operators