Related papers: Coupled Susy, pseudo-bosons and a deformed $\mathfrak{su}(1,1)$ Lie algebra

Coupled Susy, pseudo-bosons and a deformed $\mathfrak{su}(1,1)$ Lie algebra

URL: http://arxiv.org/abs/2102.11738v1
Date: Tue, 23 Feb 2021 15:03:33 GMT
Title: Coupled Susy, pseudo-bosons and a deformed $\mathfrak{su}(1,1)$ Lie algebra
Authors: Fabio Bagarello
Abstract summary: We show that a pair of operators $a$ and $b$ satisfying the equations $adagger a=bbdagger+gamma1$ and $aadagger=bdagger b+delta1$ are ladder operators. We show their connection with biorthogonal families of vectors and with the so-called $D$-pseudo bosons.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: In a recent paper a pair of operators $a$ and $b$ satisfying the equations $a^\dagger a=bb^\dagger+\gamma\1$ and $aa^\dagger=b^\dagger b+\delta\1$, has been considered, and their nature of ladder operators has been deduced and analysed. Here, motivated by the spreading interest in non self-adjoint operators in Quantum Mechanics, we extend this situation to a set of four operators, $c$, $d$, $r$ and $s$, satisfying $ dc=rs+\gamma\1$ and $cd=sr+\delta\1$, and we show that they are also ladder operators. We show their connection with biorthogonal families of vectors and with the so-called $\D$-pseudo bosons. Some examples are discussed.

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