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arXiv · 2102.11738

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

Fabio Bagarello
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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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Fabio Bagarello. 2021-02-23. Coupled Susy, pseudo-bosons and a deformed $\mathfrak{su}(1,1)$ Lie algebra. https://doi.org/10.1088/1751-8121%2Fabe910

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