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 commentarXiv admin note: text overlap with arXiv:2102.11738

References in corpus (14)

• Two families of superintegrable and isospectral potentials in two dimensions
• Intertwined isospectral potentials in an arbitrary dimension
• Intertwined Hamiltonians in Two Dimensional Curved Spaces
• Generalized ladder operators for the perturbed harmonic oscillator
• Bi-squeezed states arising from pseudo-bosons
• Ladder operators for the Ben Daniel-Duke Hamiltonians and their SUSY partners
• Tridiagonality, supersymmetry and non self-adjoint Hamiltonians
• Ladder Operators in Repulsive Harmonic Oscillator with Application to the Schwinger Effect
• Ladder operators for Klein-Gordon equation with scalar curvature term
• Ladder operators and coherent states for multi-step supersymmetric rational extensions of the truncated oscillator
• Coupled Supersymmetry and Ladder Structures Beyond the Harmonic Oscillator
• Bi-coherent states as generalized eigenstates of the position and the momentum operators
• Coupled Susy, pseudo-bosons and a deformed $\mathfrak{su}(1,1)$ Lie algebra
• Multiplication of distributions in a linear gain and loss system