Pseudo-bosons and bi-coherent states out of $\Lc^2(\mathbb{R})$

• URL: http://arxiv.org/abs/2102.05614v1
• Date: Wed, 10 Feb 2021 18:19:36 GMT
• Title: Pseudo-bosons and bi-coherent states out of $\Lc^2(\mathbb{R})$
• Authors: Fabio Bagarello
• Abstract summary: We continue our analysis on deformed canonical commutation relations and on their related pseudo-bosons and bi-coherent states. We show how to extend the original approach outside the Hilbert space $Lc2(mathbbR)$, leaving untouched the possibility of defining eigenstates of certain number-like operators. We also extend this possibility to bi-coherent states, and we discuss in many details an example based on a couple of superpotentials first introduced in citebag 2010jmp.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper we continue our analysis on deformed canonical commutation relations and on their related pseudo-bosons and bi-coherent states. In particular, we show how to extend the original approach outside the Hilbert space $\Lc^2(\mathbb{R})$, leaving untouched the possibility of defining eigenstates of certain number-like operators, manifestly non self-adjoint, but opening to the possibility that these states are not square-integrable. We also extend this possibility to bi-coherent states, and we discuss in many details an example based on a couple of superpotentials first introduced in \cite{bag2010jmp}. The results deduced here belong to the same distributional approach to pseudo-bosons first proposed in \cite{bag2020JPA}.

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