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Mathematical physics studies

Weak Pseudo-Bosons and Related Bi-coherent States

Fabio Bagarello

Published Jan 1, 2022• 0 citations
Publisher
DOI
10.1007/978-3-030-94999-0_7

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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 ℒ 2 ( 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 [30]. The results deduced here belong to the same distributional approach to pseudo-bosons first proposed in [29].

Journal of Physics Conference Series•Oct 1, 2021•8 citations
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}.
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 ℒ 2 ( 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 [30]. The results deduced here belong to the same distributional approach to pseudo-bosons first proposed in [29].